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Topic: De Rham cohomology

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	PlanetMath: Lie algebra cohomology
		Generalizing a bit, Lie algebra cohomology is just the cohomology of a particular kind of algebraic theory.
		The aim was to calculate the cohomology, in the topological sense, of a compact Lie group by using the finite-dimensional data of the corresponding Lie algebra.
		This is version 9 of Lie algebra cohomology, born on 2003-08-14, modified 2006-02-03.
	planetmath.org /encyclopedia/Cohomology2.html (647 words)

	PlanetMath: de Rham cohomology
		This action on differentiable maps makes the de Rham cohomology into a contravariant functor from the category of paracompact
		It turns out to be homotopy invariant; this implies that homotopy equivalent manifolds have isomorphic de Rham cohomology.
		This is version 5 of de Rham cohomology, born on 2004-06-12, modified 2004-10-12.
	planetmath.org /encyclopedia/DeRhamCohomology.html (123 words)

	De Rham cohomology of a smooth manifold (Site not responding. Last check: 2007-11-03)
		A vanishing theorem for the tangential de Rham cohomology...
		0521589568 From Calculus to Cohomology: De Rham Cohomology and Characteristic Cl...
		From Calculus to Cohomology : De Rham Cohomology and Characteristic Classes by I...
	www.scienceoxygen.com /math/715.html (154 words)

	Amazon.com: From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes: Books: IB Madsen,Jergen ... (Site not responding. Last check: 2007-11-03)
		De Rham cohomology is the cohomology of differential forms.
		De Rham cohomology and the theory of characteristic classes are not only two of the most important topics in mathematics, but also in theoretical physics.
		The foremost strategy for the calculation of the De Rham cohomology, the Mayer-Vietoris sequence is given, the treatment emphasizing the role of the Poincare lemma.
	www.amazon.com /Calculus-Cohomology-Rham-Characteristic-Classes/dp/0521589568 (2015 words)

	Seminar On Cohomology
		Goal: Grothendieck topologies and etale and crystalline cohomologies; applications to zeta functions and the Weil conjectures; de Rham cohomology and its variation in families; calculation of cohomology groups.
		de Rham cohomology and the Hodge to de Rham spectral sequence.
		Weil cohomology, zeta functions, cohomolgical interpretation, the zeta function of a curve and its Jacobian, variation of zeta functions, H0et and the zeta function of some zero dimensional schemes (including automorphicity), Grassmann varieties and the schubert calculus, the zeta function of Grassmann varieties.
	www.math.mcgill.ca /goren/SeminarOnCohomology.html (242 words)

	Cornell Math - Thesis Abstracts (Lie Groups)
		Abstract: This work concerns the computation of various L_2 cohomology theories, where L_2 cohomology is an analogue of de Rham cohomology on complete Riemannian manifolds which demands the forms under consideration be square integrable.
		Finally, the manifolds under study are sufficiently close to arithmetic quotients of rank one symmetric spaces that the cohomology of the links of the cusp points at infinity admits a weight space decomposition, allowing the definition of an analogue of the weighted cohomology of [GHM94] on them.
		Warped cohomology allows results on such spaces which are similar to the weighted L_2 construction of weighted cohomology (theorem A) derived on arithmetic quotients of symmetric spaces (of any rank) in [Nai99].
	www.math.cornell.edu /Research/Abstracts/lie_groups.html (1159 words)

	Hopf-cyclic homology
		Along the lines of Connes and Moscovici, we show that there is a pairing between the cyclic cohomology of a module coalgebra acting on a module algebra and closed 0-cocycles on the latter.
		It shows that passage from the cyclic homology of algebras to the cyclic cohomology of Hopf algebras is remarkably similar to passage from de Rham cohomology to the cohomology of Lie algebras via invariant de Rham cohomology [2].
		It turns out that the cyclic cohomology of Hopf algebras is a special case of the former, whereas both twisted [9] and usual cyclic cohomology are special cases of the latter.
	www.mathematik.uni-muenchen.de /~sommerh/Publikationen/HopfCyclicwww/HopfCyclicwww_en.php (580 words)

	Questions I'm thinking about
		Rigid cohomology is a cohomology theory for algebraic varieties over fields of positive characteristic that plays a role similar to that of algebraic de Rham cohomology for varieties over fields of characteristic zero.
		Rigid cohomology is a "Weil cohomology", in that it has the formal properties needed to imply the Weil Conjectures.
		Fortunately, they are separated and of finite type over a field.) Since rigid cohomology is based on de Rham cohomology in characteristic zero, understanding de Rham cohomology of suitable stacks in characteristic zero is an important prerequisite, and may be a significant task in itself.
	www-math.mit.edu /~kedlaya/questions.html (1589 words)

	Uli Walther's Research Page
		In the fall of 1998 I was a guest at the Mathematical Sciences Research Institute, MSRI.
		Local cohomology and pure morphisms With A. Singh (to appear in Ill. J.
		Current work is on local cohomology of toric varieties; hypergeometric systems; b-functions and homological properties of $D$-modules.
	www.math.purdue.edu /~walther/research/index.html (582 words)

	[No title]
		More specifically, he represented the cohomology of a compact Riemann surface with the help of holomorphic differential forms of degree one, that is, in terms of a local coordinate $z$, forms of the type $f(z)\,dz$ where $f$ is holomorphic.
		De Rham showed that for any differentiable manifold cohomology can be defined with the help of smooth differential forms.
		Characteristic classes are usually defined with the aid of differential form using de Rhams theorem.
	www.maths.lth.se /matematiklu/personal/jaak/derham.html (570 words)

	Absolute Hodge cycles (Site not responding. Last check: 2007-11-03)
		In joint work with H. Esnault we explore the relation between this notion and the notion of absolute de Rham cycle which we have introduced.
		The latter is an infinitesimal analogue of the notion of absolute Hodge cycles and should prove easier to study in relation with the Hodge conjecture.
		In particular, we were able to construct the Leray spectral sequence for de Rham cohomology, prove the comparison theorem with singular cohomology and also demonstrate the coniveau spectral sequence used (without proof) in the paper ([
	www.imsc.res.in /~kapil/work/node10.html (195 words)

	Amazon.com: RHAM (Site not responding. Last check: 2007-11-03)
		From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes by IB Madsen, Jergen Tornehave, and Madsen/Tornehave (Paperback - Jan 1, 1997)
		Hodge Theory in the Sobolev Topology for the De Rham Complex (Memoirs of the American Mathematical Society) by Luigi Fontana, Steven G. Krantz, and Marco M. Peloso (Paperback - Jun 1998)
		The petition of Henry C. De Rham, to the General Assembly of Rhode-Island, to except Paul Daniel Gonsalve Grand d'Hauteville, from the operation of the...
	www.amazon.com /s?ie=UTF8&keywords=RHAM&tag=acronymfinder-20&index=blended&link_code=qs&page=1 (688 words)

	Leibniz Cohomology for Differentiable Manifolds, by Jerry Lodder
		Leibniz Cohomology for Differentiable Manifolds, by Jerry Lodder
		The goal of this paper is to extend Loday's Leibniz cohomology from a Lie algebra invariant to an invariant for differentiable manifolds so that Leibniz cohomology is a non-commutative version of de Rham cohomology.
		Leibniz cohomology, HL^, is no longer a homotopy invariant---in fact the first obstruction to the homotopy invariance of HL^(R^n) is the universal Godbillon-Vey invariant in dimension 2n+1.
	www.math.uiuc.edu /K-theory/0159 (147 words)

	Math Forum Discussions - User Profile for: horosiewic_@_mail.com
		Re: de Rham cohomology of R^2 minus two points
		de Rham cohomology of R^2 minus two points
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /kb/profile.jspa?userID=169945 (65 words)

	Lang: Two theorems on de Rham cohomology
		Lang, William E. Two theorems on de Rham cohomology.
		: On the de Rham cohomology of algebraic varieties, Publ.
		: The first de Rham cohomology group and Dieudonné modules, Ann.
	www.numdam.org /numdam-bin/item?id=CM_1980__40_3_417_0 (79 words)

	[No title]
		Okay, we'll first look at the de Rham complex on R^n before we move on to more general manifolds.
		Omega^(R^n), together with d, is called the de Rham* complex on R^n.
		If it's necessary to distinguish between a form and its cohomology class, we will let the former be w and the latter be [w] [17:40]
	br.endernet.org /~loner/difftop/kimderham.txt (2997 words)

	On twisted de Rham cohomology, Alan Adolphson, Steven Sperber
		On twisted de Rham cohomology, Alan Adolphson, Steven Sperber
		[KI] M. Kita, On vanishing of the twisted rational de Rham cohomology associated with hypergeometric functions,Nagoya Math.
		[KO] A. G.Kouchnirenko, Polyedres de Newton et nombres de Milnor, Invent.
	projecteuclid.org /getRecord?id=euclid.nmj/1118771659 (255 words)

	Algebraic Topology in a Differential Geometry - Cambridge University Press
		Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required.
		The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples.
		This book will be suitable for graduate students taking courses in algebraic topology and in differential topology.
	www.cambridge.org /catalogue/catalogue.asp?ISBN=0521317142 (168 words)

	Math 262
		Universal Coefficients Theorem (for both cohomology and homology)
		Equivalence of Cech, singular, and De Rham cohomology
		Kenneth S. Brown, Cohomology of Groups, Springer-Verlag 1982.
	www.cgtp.duke.edu /~psa/cls/262 (117 words)

	44a
		, we want to count points using `de Rham' cohomology.
		We will demonstrate Monsky-Washnitzer cohomology (a kind of rigid cohomology for smooth affine varieties).
		are finite-dimensional, but it is not obvious; it relies upon relating this cohomology to rigid cohomology for proper varieties, namely, crystalline cohomology which we know is finite-dimensional for other reasons.
	www.aimath.org /WWN/primesinp/articles/html/44a (148 words)

	Table of contents for Library of Congress control number 96028589
		Table of contents for Library of Congress control number 96028589
		Table of contents for From calculus to cohomology : de Rham cohomology and characteristic classes / Ib Madsen and Jrgen Tornehave.
		Bibliographic record and links to related information available from the Library of Congress catalog
	www.loc.gov /catdir/toc/cam026/96028589.html (84 words)

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