Obstructions to homotopy equivalences
Stephen Halperin,Jim Stasheff +1 more
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In this article, an obstruction theory is developed to decide when an isomorphism of rational cohomology can be realized by a rational homotopy equivalence (either between rationally nilpotent spaces, or between commutative graded differential algebras).About:
This article is published in Advances in Mathematics.The article was published on 1979-06-01 and is currently open access. It has received 263 citations till now. The article focuses on the topics: Equivariant cohomology & Eilenberg–MacLane space.read more
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Braid group actions on derived categories of coherent sheaves
Paul Seidel,Richard P. Thomas +1 more
TL;DR: In this paper, the authors give a construction of braid group actions on coherent sheaves on a variety of manifolds and show that these actions are always faithful when the manifold is smooth.
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Braid group actions on derived categories of coherent sheaves
Paul Seidel,Richard P. Thomas +1 more
TL;DR: In this article, the authors give a construction of braid group actions on coherent sheaves on a variety of manifolds and show that these actions are always faithful when the manifold is an elliptic curve.
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Algebraic models in geometry
TL;DR: A Florilege of Geometric Applications as mentioned in this paper is a collection of geometrical applications in which Lie Groups and Homogeneous Spaces have been used for a wide range of purposes, e.g.
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Homotopy Limits, Completions and Localizations
A. K. Bousfield,Daniel M. Kan +1 more
TL;DR: The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X, which coincides up to homotopy with the p-profinite completion of Quillen and Sullivan as mentioned in this paper.
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Rational homotopy theory
TL;DR: The rational homotopy groups tensored with Q were studied in this paper, where it was shown that the torsion of these groups is not a strong predictor of the rationality of the groups.
Book
Simplicial objects in algebraic topology
TL;DR: Simplicial Objects in Algebraic Topology as discussed by the authors has been the standard reference for the theory of simplicial sets and their relationship to the homotopy theory of topological spaces.
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Real Homotopy Theory of Kähler Manifolds.
TL;DR: In this paper, the De Rham Complex of a Compact K~ihler Manifold has been shown to be a homotopy theory of differential algebras.