Morse inequalities for R-constructible sheaves

Schapira, Pierre; Tose, Nobuyuki

doi:10.1016/0001-8708(92)90022-d

Cited by 4 publications

(2 citation statements)

References 4 publications

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“…In this subsection, we give the Morse-Bott inequality for sheaves, which is a slight generalization of the Morse inequality for sheaves by Kashiwara-Schapira [KS90, Proposition 5.4.20] and was proved by Schapira-Tose [ST92]. For a bounded complex W of k-vector spaces with finite-dimensional cohomology and k ∈ Z, we set…”

Section: Morse-bott Inequality For Sheaves ([St92])mentioning

confidence: 99%

Compact Exact Lagrangian Intersections in Cotangent Bundles via Sheaf Quantization

Ike

2019

Publ. Res. Inst. Math. Sci.

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We show that the cardinality of the transverse intersection of two compact exact Lagrangian submanifolds in a cotangent bundle is bounded from below by the dimension of the Hom space of sheaf quantizations of the Lagrangians in Tamarkin's category. Our sheaf-theoretic method can also deal with clean and degenerate Lagrangian intersections. k∈Z dim H k (M ; L) (1.4) for any rank 1 locally constant sheaf L on M over any field k. In particular, #(L 1 ∩ L 2 ) ≥ k∈Z dim H k (M ; k).

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Section: Morse-bott Inequality For Sheaves ([St92])mentioning

confidence: 99%

Compact Exact Lagrangian Intersections in Cotangent Bundles via Sheaf Quantization

Ike

2019

Publ. Res. Inst. Math. Sci.

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“…Until the end of this subsection as well as in Section 4.4 we assume that k is a field. The classical Morse inequalities are extended to sheaves (see [23] and [13,Prop. 5.4.20]).…”

Section: Morse Lemma and Morse Inequalities ([13 §54])mentioning

confidence: 99%

Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems

Guillermou¹,

Kashiwara²,

Schapira³

2012

Duke Math. J.

187

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Numerical control over complex analytic singularities

Massey¹

2003

Memoirs of the AMS

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In undergoing this life, many people always try to do and get the best. New knowledge, experience, lesson, and everything that can improve the life will be done. However, many people sometimes feel confused to get those things. Feeling the limited of experience and sources to be better is one of the lacks to own. However, there is a very simple thing that can be done. This is what your teacher always manoeuvres you to do this one. Yeah, reading is the answer. Reading a book as this numerical control over complex analytic singularities and other references can enrich your life quality. How can it be?

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Morse inequalities for R-constructible sheaves

Cited by 4 publications

References 4 publications

Compact Exact Lagrangian Intersections in Cotangent Bundles via Sheaf Quantization

Compact Exact Lagrangian Intersections in Cotangent Bundles via Sheaf Quantization

Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems

Numerical control over complex analytic singularities

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