Singular Cohomology

2018 ◽  
pp. 174-194
Author(s):  
Marvin J. Greenberg ◽  
John R. Harper
Keyword(s):  
Singular Cohomology

Fourier-Mukai Transforms in Algebraic Geometry

2007 ◽  
Author(s):  
D. Huybrechts
Keyword(s):  
Algebraic Geometry ◽  
Smooth Projective Variety ◽  
Derived Category ◽  
Point Of View ◽  
Basic Knowledge ◽  
Research Directions ◽  
Coherent Sheaves ◽  
Geometric Point ◽  
Singular Cohomology

This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.

scholarly journals On the axiomatic systems of singular cohomology theory

2020 ◽  
Vol 275 ◽  
pp. 107014
Author(s):  
Anzor Beridze ◽  
Leonard Mdzinarishvili
Keyword(s):  
Cohomology Theory ◽  
Singular Cohomology ◽  
Axiomatic Systems

Algebraic EHP Sequences Revisited

2018 ◽  
Vol 62 (3) ◽  
pp. 625-640
Author(s):  
Thế Cu’ò’ng Nguyễn
Keyword(s):  
Algebraic Topology ◽  
Homotopy Theory ◽  
Injective Resolution ◽  
Singular Cohomology

AbstractThe algebraic EHP sequences, algebraic analogues of the EHP sequences in homotopy theory, are important tools in algebraic topology. This note will outline two new proofs of the existence of the algebraic EHP sequences. The first proof is derived from the minimal injective resolution of the reduced singular cohomology of spheres, and the second one follows Bousfield's idea using the loop functor of unstable modules.

Singular cohomology inL

1977 ◽  
Vol 26 (3-4) ◽  
pp. 313-319 ◽  
Author(s):  
Howard L. Hiller ◽  
Saharon Shelah
Keyword(s):  
Singular Cohomology

scholarly journals Morita cohomology

2014 ◽  
Vol 158 (1) ◽  
pp. 1-26 ◽  
Author(s):  
JULIAN V. S. HOLSTEIN
Keyword(s):  
Topological Space ◽  
Loop Space ◽  
Perfect Complexes ◽  
Singular Cohomology

AbstractWe consider two categorifications of the cohomology of a topological spaceXby taking coefficients in the category of differential graded categories. We consider both derived global sections of a constant presheaf and singular cohomology and find the resulting dg-categories are quasi-equivalent and moreover quasi-equivalent to representations in perfect complexes of chains on the loop space ofX.

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