Sheaves in Topology

By Alexandru Dimca. 2004

543 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6c21cce8e7d3caad0b780bbc3ccc036de60f33a6

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Citations in the corpus

Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants (2010, background): “f!QX has weights 6 0. In particular, the conditions of the Proposition hold for a pair (X,f) such that X is smooth and f : X →A1 C is proper. More generally, f could be cohomologically tame (see e.g. [13], [45]), e.g. when Xis an aﬃne space and fis a quasi-homogeneous polynomial with isolated singul”
Symmetries and stabilization for sheaves of vanishing cycles (2012, background): “4 with a general introduction to constructible complexes and perverse sheaves on C-schemes, the nearby and vanishing cycle functors, and perverse sheaves of vanishing cycles PV • U,f on C-schemes, following Dimca [14].”
A geometric degree formula for A-discriminants and Euler obstructions of toric varieties (2008, methodology): “We hope that we could show the power and the beauty of the sheaf-theoretical methods (see for example, [6], [16] and [18]) by proving them functorially.”
A theory of generalized Donaldson–Thomas invariants (2008, background): “Partial results in this case can be found in Dimca and Szendrői [19] and Behrend, Bryan and Szendrői [4], see in particular [4, Rem.”
A ‘Darboux theorem’ for shifted symplectic structures on derived Artin stacks, with applications (2013, methodology): “For K = C one can define perverse sheaves using the complex analytic topology as in Dimca [7], and then A can be essentially arbitrary, e.g.”
Cohomology of the space of commuting n-tuples in a compact Lie group (2006, background): “Y) ∼=H(X). Proof. Recall that for simplicial complexes, singular cohomology over S is naturally isomorphic to sheaf cohomology of SX, the constant sheaf on Xwith coeﬃcients in S. Leray’s theorem (see [Di]) says that the sheaf cohomology, H(X,SX), is computable as the limit of aspectral sequence E∗,∗”
Koszul Complexes and Pole Order Filtrations (2011, background): “1) H(Ff )λk = H (U, Lk) where in the LHS we have the corresponding eigenspace and in the RHS we have the twisted cohomology of U with coefficients in Lk, see for details [12], Proposition 6.”