
	Where results make sense

Topic: Chern class

Related Topics

Finsler metric

Ricci curvature tensor

List of famous Chinese Americans

In the News (Tue 29 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Chern class - Wikipedia, the free encyclopedia
		That is, Chern classes are cohomology classes in the sense of de Rham cohomology.
		In algebraic geometry, this classification of (isomorphism classes of) complex line bundles by the first Chern class is a crude approximation to the classification of (isomorphism classes of) holomorphic line bundles by linear equivalence classes of divisors.
		The Chern classes of M are thus defined to be the Chern classes of its tangent bundle.
	en.wikipedia.org /wiki/Chern_class (1878 words)

	Chern class (Site not responding. Last check: 2007-10-31)
		In algebraic topology, the Chern classes of a complex vector bundle V on a topological space X are defined in the theory of characteristic classes.
		Chern classes also arise naturally in algebraic geometry.
		The intuitive meaning of the Chern class concerns 'required zeroes' of a section of a vector bundle: for example the theorem saying one can't comb a hairy ball flat.
	bopedia.com /en/wikipedia/c/ch/chern_class.html (105 words)

	Pontryagin class - Wikipedia, the free encyclopedia
		In mathematics, the Pontryagin classes are certain characteristic classes.
		Pontryagin classes have a meaning in real differential geometry — unlike the Chern class, which assumes a complex vector bundle at the outset.
		The Pontryagin classes of a smooth manifold are defined to be the Pontryagin classes of its tangent bundle.
	en.wikipedia.org /wiki/Pontrjagin_class (447 words)

	UC Berkeley Mathematics
		Chern classes and later advances in differential geometry have now found applications in fields as diverse as string theory in theoretical physics and computer graphics.
		Shiing-Shen Chern, the famed UC Berkeley mathematician whose name is immortalized in the "Chern classes" of differential geometry, died Friday in Tianjian, China.
		A Chern class is a numerical invariant attached to complex manifolds -- an object of study in differential geometry.
	math.berkeley.edu /index.php?module=announce&ANN_user_op=view&ANN_id=31 (1326 words)

	Chern (Site not responding. Last check: 2007-10-31)
		Chern Number -- from MathWorld Chern Number -- from MathWorld The Chern number is defined in terms of the Chern class of a manifold as follows.
		The Chern classes of a complex manifold are the Chern classes of its tangent bundle.
		Chern Classes and Extraspecial Groups Chern Classes and Extraspecial Groups The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p.
	www.99hosted.com /names6841.html (293 words)

	[No title]
		TRANSFER AND CHERN CLASSES FOR EXTRASPECIAL p-GROUPS DAVID JOHN GREEN AND PHAM ANH MINH Abstract.In the cohomology ring of an extraspecial p-group, the subring generated by Chern classes and transfers is studied.
		For integral cohomology however, the problem remains open, and the significance of Corollary 8.2 is that this subring is the biggest studi* *ed to date in the cohomology ring of an extraspecial p-group.
		In Theorem 5.2, an elegant formula is obtained relating the Chern classes and the Or;OE, and in Theorem 7.2 we show that the pth power of any Chern class or any Or;OElies in the subring ____________ Date: 15 November 1996.
	hopf.math.purdue.edu /Green-Minh/gm_transfer.txt (839 words)

	[No title]
		This is the top Chern class of the # quotient of the 5th symmetric power of the universal quotient on the # Grassmannian of 2 planes in P^5 by the subbundle of quintic containing the # tautological conic over the moduli space of conics.
		rank - the rank of a sheaf chern - the chern class(es) of a sheaf segre - segre class(es) of a sheaf.
		The Chern classes of the bundle are obtained by concatenation of the degree of the class with name.
	www.math.sunysb.edu /~sorin/online-docs/schubert/schubertmanual.txt (5882 words)

	[No title]
		But a recent thread turned to Chern classes, which is not only mathematics but a part of mathematics I understand moderately well, so after a couple of email messages I have been persuaded to write in with some explanatory material.
		So that's what a "cohomology class" is (may be considered to be): it's a (homotopy equivalence class of) map from the given space X into a particular and peculiar space K(G,n).
		I want to stress that many of the facts one might wish to prove about Chern classes is now rather easy, or at least can be pushed away from bundels altogether and reduced to certain calculations about the classifying spaces.
	www.math.niu.edu /~rusin/known-math/00_incoming/chern_cl (2177 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-31)
		The characteristic class determined by an even symmetric polynomial in the Wu generators can be expressed in Pontryagin classes as follows.
		Moreover, rational Pontryagin classes were defined (see [4]) for piecewise-linear manifolds (possibly with a boundary).
		From this the topological invariance of rational Pontryagin classes follows, as well as a disproof of the fundamental hypothesis of combinatorial topology (the Hauptvermutung).
	eom.springer.de /p/p073750.htm (732 words)

	Springer Online Reference Works
		A characteristic class defined for complex vector bundles.
		, and the Chern polynomial is the expression
		This important property, which enables one to define the Chern character, does not hold in generalized cohomology theories.
	eom.springer.de /c/c022030.htm (541 words)

	[No title]
		We also realize Chern classes in the case where $X$ is smooth, and establish a universal relation between the Chern character and the Chern classes.
		Using the Chern character studied by the authors in a companion paper, we show that there is a rational isomorphism between holomorphic $K$-theory and the appropriate "morphic cohomology", defined by Lawson and Friedlander.
		The class is shown to be the (Z/2Z)-equivariant Chern class on Atiyah's KR-theory.
	www.lehigh.edu /~dmd1/h12 (1187 words)

	Math 433 Homepage (Site not responding. Last check: 2007-10-31)
		These are the class notes to Math 433 - The Geometry of Vector Bundles and an Introduction to Gauge Theory - during the spring semester of 1998 at the The University of Illinois at Urbana Champaign.
		Chern characters as a map between bundles and cohomology.
		The relationship between Pontrjagin classes and Chern classes of a complexified bundle.
	www.math.uiuc.edu /~cwillett/bundles (883 words)

	[No title]
		An important theorem says this class is necessarily an integral class, that is, it comes from an element of the 2nd cohomology with integer coefficients; moreover, isomorphism classes of line bundles over a manifold are in one-to-one correspondence with elements of its 2nd cohomology with integer coefficients.
		But the nth Chern class is an element of the 2nth cohomology group, so the odd cohomology groups don't play a major role here.
		The beauty of 2nd cohomology is that integer classes in the 2nd cohomology of M correspond to line bundles on M; there is, in other words, a very nice geometrical picture of 2nd cohomology classes.
	math.ucr.edu /home/baez/twf_ascii/week25 (2476 words)

	[No title]
		The class can be detected by restricting to the cyclic groups C_n contained in S_n as the powers of an n-cycle.
		The standard representation of U_n restricts to the regular representation of C_n, with Chern polynomial \prod_{j=0}^{n-1} (1+jxt) The required restriction is the coefficient of t^2, this is 2x^2 mod 3, for n=3 and 3x^2 mod 4 for n=4.
		The Chern classes of any rational representation of a finite group have order dividing the denominators of Bernoulli numbers by Galois invariance.
	www.lehigh.edu /~dmd1/cs1221.txt (148 words)

	file_nav_name Encyclopedia Index
		In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of line...
		In topology and related branches of mathematics, a totally bounded space, or precompact space, is a space that can be c...
		The spectrum of a C-algebra or dual of a C-algebra A, denoted Ã, is the set of unitary equivalence classes of ir...
	www.brainyencyclopedia.com /topics/space.html (8659 words)

	M&I: Electronic mail #3 of 10 (Site not responding. Last check: 2007-10-31)
		On a spin compact oriented 4-manifold X, fix a hermitian line bundle L with chern class divisible by 2.
		Cut out a ball around it in N; then the boundary down on M is S^{4m-1}/S^1 = CP^{2m-1}, and the chern class of N restricts to a generator.
		The integral of its top power over CP^{2m-1} is therefore 1, but since the chern class extends over all of M minus the singular point, this contradicts Stokes's theorem.
	www.ugrad.math.ubc.ca /openhse/mail/mail3.html (615 words)

	[No title]
		Well, this is not so bad, since the nth Chern class belongs to the 2nth cohomology group.
		To briefly sketch the theory: the nth Chern class of a complex vector bundle is formed by picking a connection on it, forming the curvature F, and doing something with F ^ F ^...
		Line bundles are classified by their 1st Chern class and all the higher Chern classes are trivial.
	www.math.niu.edu /~rusin/known-math/00_incoming/phew (2022 words)

	[No title]
		Whenever you have a complex line bundle over a space X, you get an invariant called its "first Chern class" which lives in H^2(X), and this invariant is sufficiently powerful to completely classify such line bundles.
		If a generalized cohomology theory is multiplicative and there's an element c of h^2(CP^infinity) that acts like the first Chern class of the universal line bundle, we call the theory "complex oriented".
		This is exactly like the usual first Chern class of our line bundle, except now we're using a generalized cohomology theory instead of ordinary cohomology.
	math.ucr.edu /home/baez/twf_ascii/week150 (2788 words)

	No Title (Site not responding. Last check: 2007-10-31)
		Self-dual Chern-Simons theories form a new class of self-dual gauge theories and provide a field theoretical formulation of anyonic excitations in planar (i.e.
		These Chern-Simons theories are particular to planar systems and have therefore received added research impetus from recent experimental and theoretical breakthroughs in actual planar condensed matter systems such as the quantum Hall effect.
		These Lecture Notes give a pedagogical introduction to the basic properties of the special class of Chern-Simons theories known as ``self-dual'' Chern-Simons theories, concluding with an overview of more advanced results and an extensive bibliography.
	www.phys.uconn.edu /~dunne/dunne_book.html (196 words)

	Abstract (Site not responding. Last check: 2007-10-31)
		Abstract: We study a general class of degeneracy loci associated to a sequence of vector bundles with maps between them and arbitrary rank conditions on the maps and their compositions.
		The cohomology classes of such loci are described by polynomials in the Chern classes of the vector bundles.
		We furthermore conjecture that all coefficients are positive and given by counting tableaux.
	www-math.mit.edu /alg_geom_sem/Buch.html (88 words)

	Atlas: A dilogarithmic formula for the Cheeger-Chern-Simons class by Christian Zickert (Site not responding. Last check: 2007-10-31)
		A formula by Dupont computes the universal class using Rogers' dilogarithm, but his formula is only correct modulo Q. In a recent paper Neumann extends the work by Dupont and obtains a formula without this indeterminacy.
		The new formula can be applied directly to a homology class in the bar complex.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cass-14.
	atlas-conferences.com /cgi-bin/abstract/cass-14 (130 words)

	Asuke: A remark on the Bott class
		— Characteristic classes of transversely homogeneous foliations, Trans.
		- On characteristic classes of conformal and projective foliations, J.
		- On characteristic classes of riemannian, conformal and projective foliations, J.
	www.numdam.org /numdam-bin/item?id=AFST_2001_6_10_1_5_0 (155 words)

	Brodzki, Mathai, Rosenberg & Szabo on D-Branes, RR-Fields and Duality \| The String Coffee Table
		which is roughly the Chern class of the Chan-Paton bundle times the square root of the Todd class.
		The authors of the present paper manage to find an analogue of the Todd class for general
		cup-multiplying this Chern class with half of the Atiyah-Hirzebruch class of spacetime
	golem.ph.utexas.edu /string/archives/000879.html (941 words)

	National Taiwan University
		Maintained by 汪瑜(Jane Y. Chern, Class of 84)
		Let me know if there were any errors.
		*Class of 88,在San Diego and San Francisco, 有一場小聚會,照片在下欄Gallery Section刊出;
	members.cox.net /janechern/ntumtalumni.htm (472 words)

	DC MetaData for: Verdier-Riemann-Roch for Chern Class and Milnor Class (Site not responding. Last check: 2007-10-31)
		DC MetaData for: Verdier-Riemann-Roch for Chern Class and Milnor Class
		In this paper we deal with a Chern class version of this, with the
		replaced by the Chern-Schwartz-MacPherson class transformation $c_: F \to H_$.
	www.esi.ac.at /Preprint-shadows/esi933.html (85 words)

	Physics 230 Course Information
		Sectors classified by winding number and magnetic flux.
		No class 1/12 and 1/14 due to String Theory at the Millennium Conference.
		Energetics and structure of the vortices of the abelian Higgs model.
	www.theory.caltech.edu /people/preskill/ph230/index.html (1525 words)

	A Remark On The Chern Class Of A Tensor Product (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		A Remark On The Chern Class Of A Tensor Product (ResearchIndex)
		A Remark On The Chern Class Of A Tensor Product
		Online articles have much greater impact More about CiteSeer Add search form to your site Submit documents Feedback
	citeseer.ifi.unizh.ch /14266.html (181 words)

Try your search on: Qwika (all wikis)