
	Where results make sense

Topic: Poincar duality

Related Topics

Henri Poincar

The Poincar Conjecture

Poincar group

Poincar duality

Raymond Nicolas Landry Poincare

Poincar Birkhoff Witt theorem

Poincar map

Poincar duality theorem

Poincar covariance

Nicolas Antoinin H l ne Poincar

Raimond Poincar

In the News (Wed 15 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Topology - Wikipedia, the free encyclopedia
		Topology has introduced a new geometric language (simplicial complexes, homotopy, cohomology, Poincaré duality, fibrations, vector bundles, sheaves, characteristic classes, Morse functions, homological algebra, spectral sequences).
		Georg Cantor, the inventor of set theory, had begun to study the theory of point sets in Euclidean space, in the later part of the 19th century, as part of his study of Fourier series.
		Henri Poincaré published Analysis Situs in 1895, introducing the concepts of homotopy and homology.
	en.wikipedia.org /wiki/Topology (1876 words)

	[No title]
		Broadly speaking Poincar\'e duality for classical manifolds consists in the isomorphism of homology and cohomology.
		It is a fascinating fact that the physical ``duality'' of the electroweak and chromodynamics sectors of elementary particle physics can be viewed as an example (indeed the historically first example!) of the non-commutative generalization of Poincar\'e duality.
		The convincing interpretation of the electroweak-chromodynamical duality as a case of non-commutative Poincar\'e duality, with concomitant enrichment of the mathematical notion of non-commutative space, is a beautiful feature.
	www.ma.utexas.edu /mp_arc/html/papers/94-264 (9786 words)

	[No title]
		Let S = S[V #] be the symmetric algebra on V # the k-dual of V, and R = S^W the ring of invariants of under the natural action of W on S. Define P* to be the quotient algebra S i\tensor_R k.
		If the characteristic of k is zero or prime to the order of W and P* satisfies Poincar'e duality, then R is isomorphic to a polynomial algebra on r generators.
		Steinberg [9] has shown that R is polynomial if k is the field of complex numbers and the quotient algebra P* = S\tensor_R k satisfies Poincar'e duality (1.3).
	www.lehigh.edu /~dmd1/h0606 (919 words)

	Albert Einstein as a Philosopher of Science - Physics Today December 2005
		Schlick and Reichenbach's eventual answer was based mainly on Poincaré's version of conventionalism.
		They argued that what the knower contributes are the definitions linking fundamental theoretical terms like "straight line segment" with empirical or physical notions like "path of a ray of light." But, they contended, once such definitions are stipulated by convention, the empirical truth or falsity of all other assertions is uniquely fixed by experience.
		Only late in 1924, when Einstein first read Satyendra Bose's new derivation of the Planck radiation formula, did he grasp that what was implied was a new quantum statistics, in which particles fail to be independent not because of some exotic interaction but because their identity makes them indistinguishable.
	www.physicstoday.org /vol-58/iss-12/p34.html (4881 words)

	Duality Relating Spaces of Algebraic Cocycles and Cycles, by Eric M. Friedlander and H. Blaine Lawson (Site not responding. Last check: 2007-11-01)
		In this paper a fundamental duality is established between algebraic cycles and algebraic cocycles on a smooth projective variety.
		If $X$ is a smooth projective variety of dimension $n$, our duality map induces isomorphisms $L^sH^k(X) \to L_{n-s}H_{2n-k}(X)$ for $2s\leq k$ which carry over via natural transformations to the Poincar\'e duality isomorphism $H^k(X;{\bf Z}) \to H_{2n-k}(X;{\bf Z})$.
		Among applications presented are the determination of the homotopy type of certain algebraic mapping complexes and a computation of the group of algebraic $s$-cocycles modulo algebraic equivalence on a smooth projective variety.
	www.math.uiuc.edu /K-theory/0047 (167 words)

	Online Course Synopsis Handbook (Site not responding. Last check: 2007-11-01)
		duality, plus topics selected from: higher homotopy groups, obstruction theory, Hurewicz and Whitehead theorems, and characteristic classes.
		Differential forms, de Rham cohomology, Poincaré duality, vector bundles, Thom isomorphism, characteristic classes
		This course is essential for graduate students interested in studying Algebraic Topology, Differential Geometry, and Mathematical Physics, and would also be important for students interested in Algebraic Geometry.
	www.math.duke.edu /graduate/courses/fall06/math262 (88 words)

	essay23
		Nevertheless, Henri Poincaré and many other scientists did not regard the aether as "superfluous." But by 1920, one could say that the aether hypothesis was rejected.
		Now, some 85 years later, another look indicates that all of space may be filled, after all, by a mysterious substance, the aether.
		Compared to the photon experiment, the apparatus displays two changes: an electron requires a high vacuum, and its energy is absorbed by a fluorescent screen that, in turn, “lights up” the photographic film.
	www.siddeutsch.org /essay23.html (4149 words)

	Citebase - T-spectra and Poincaré Duality (Site not responding. Last check: 2007-11-01)
		Frank Adams introduced the notion of a complex oriented cohomology theory represented by a commutative ring-spectrum and proved the Poincaré Duality theorem for this general case.
		In the current paper we consider oriented cohomology theories on algebraic varieties represented by multiplicative symmetric T-spectra and prove the Duality theorem, which mimics the result of Adams.
		This result is held, in particular, for Motivic Cohomology and Algebraic Cobordism of Voevodsky.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0506017 (121 words)

	Proceedings of the American Mathematical Society
		G.E. Bredon, Fixed point sets of actions on Poincaré duality spaces, Topology 12 (1973), 159-175 MR 48:9708
		B. Hanke, Poincaré duality and deformations of algebras, Contemp.
		Keywords: Group action, Betti number, Poincar\'e duality space
	e-math.ams.org /proc/2003-131-10/S0002-9939-03-06856-4/home.html (238 words)

	Nineteenth Century Geometry
		All this follows, of course, from the very nature of axiomatics, as explained in the passage quoted from Pasch.
		(In projective space geometry, duality holds for points and planes.) The same result is secured, of course, by exchanging not the words, but their meanings.
		In a lecture "On the hypotheses that lie at the foundation of geometry", delivered to the Faculty of Philosophy at Göttingen in 1854 and posthumously published in 1867, Bernhard Riemann (b.
	plato.stanford.edu /entries/geometry-19th (4771 words)

	Tuning-Math Archive Section 11: 10350 - 10374
		Message: 10356 - Contents - Hide Contents Date: Sat, 21 Feb 2004 05:13:55 Subject: poincare duality From: Paul Erlich I think Mathworld could use your help with this one, Gene: Poincar Duality -- from MathWorld * [with cont.]
		In all of which I managed to lose sight of my original goal of relevance to music, but the encyclopedia is much improved in the area of special functions relevant to number theory.
		However, I see that immediately afterward he moved material from the Grassmann algebra page to this one, giving it an entire new introductory section, and thereby making it more concrete, just as we had discussed.
	www.robertinventor.com /tuning-math/s__11/msg_10350-10374.html (1904 words)

	P.B. Stark: Curriculum Vitae
		Inference in infinite-dimensional inverse problems: Discretization and duality, J.
		Data Reduction and Inverse Problems in Helioseismology, Workshop "Statistics of inverse problems," Institut Henri Poincaré, 28-29 May, Paris, France.
		Duality and Discretization Error, Conference on Mathematical Geophysics, Blanes, Spain
	www.stat.berkeley.edu /~stark/bio.htm (4041 words)

	Poincaré duality pairs of dimension three
		On 3-dimensional Poincar{é} duality complexes and 2-knot groups,
		Homotopy theory and duality (Gordon and Breach, New York, London, Paris, 1965).
		Three dimensional Poincar{é} complexes: Homotopy classification and splitting,
	www.austms.org.au /Publ/Bulletin/V72P2/722-5232-Bleile/index.shtml (104 words)

	Poincar? Algebras Macauley Sys Ops - Dagmar M. Meyer - Larry Smith - Adobe Reader PDF eBook
		Home > eBook Categories > Science & Technology > Mathematics > Adobe Reader PDF eBooks > Dagmar M. Meyer > Larry Smith > Poincar?
		duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay's dual systems in the study of irreducible ideals in polynomial algebras.
		These two ideas are tied together using basic commutative algebra involving Gorenstein algebras.
	www.ebookmall.com /ebook/189812-ebook.htm (775 words)

Try your search on: Qwika (all wikis)