A sheaf-theoretic model for SL(2,C) Floer homology

Abouzaid, Mohammed; Manolescu, Ciprian

doi:10.48550/arxiv.1708.00289

Cited by 8 publications

(14 citation statements)

References 65 publications

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“…The previous complex was considered in [AM20] where it was called the complexified instanton Floer homology of N .…”

Section: D A-modelmentioning

confidence: 99%

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Batalin--Vilkovisky quantization and supersymmetric twists

Safronov¹,

Williams²

2021

Preprint

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We show that a family of topological twists of a supersymmetric mechanics with a Kähler target exhibits a Batalin-Vilkovisky quantization. Using this observation we make a general proposal for the Hilbert space of states after a topological twist in terms of the cohomology of a certain perverse sheaf. We give several examples of the resulting Hilbert spaces including the categorified Donaldson-Thomas invariants, Haydys-Witten theory and the 3-dimensional A-model.

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“…The previous complex was considered in [AM20] where it was called the complexified instanton Floer homology of N .…”

Section: D A-modelmentioning

confidence: 99%

“…The cohomology of the perverse sheaf P X has been used to define cohomological Hall algebras of quivers with potentials [KS11], categorified Donaldson-Thomas invariants [Ben+15] and complexified Floer homology [AM20].…”

Section: Introductionmentioning

confidence: 99%

Batalin--Vilkovisky quantization and supersymmetric twists

Safronov¹,

Williams²

2021

Preprint

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“…The Heegaard-splitting approach has been studied by Boyer-Nicas [BN90], Walker [Wal92], Cappell-Lee-Miller [CLM90], and Curtis [Cur94]. More recently, Abouzaid-Manolescu [AM17] studied the intersection of SL 2 (C) character varieties arisen from Heegaard splittings and obtained a sheaf-theoretic 3-manifold invariant. On the gauge theory side, Boden-Herald [BH98] defined an SU(3) Casson invariant for integer homology spheres by introducing real-valued correction terms on the reducible critical orbits.…”

Section: Introductionmentioning

confidence: 99%

A symplectic formula of generalized Casson invariants

Bai

2021

Preprint

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Suppose Y is an integer homology 3-sphere, Taubes [Tau90] proved that the number of irreducible critical orbits of the perturbed Chern-Simons functional on Y , counted with signs, is equal to the algebraic intersection number of two character varieties associated with Heegaard splittings when the structure group is SU(2). Taubes' result established a relationship between gauge theory and the Casson invariant. This article proves an analogous identification result for SU(n) generalized Casson invariants. As a special case, we show that the SU(3) Casson invariant of Boden-Herald [BH98] can be equivalently calculated by taking an appropriate intersection number of Lagrangian submanifolds.

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“…A similar category has been introduced by Moore and Tachikawa [MT12] in the holomorphic setting, and could serve as a target for SLp2, Cq analogues of instanton homology, as introduced in [AM17,CM18].…”

Section: Introductionmentioning

confidence: 99%

A two-category of Hamiltonian manifolds, and a (1+1+1) field theory

Cazassus¹

2019

Preprint

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We define an extended field theory in dimensions 1 `1 1, that takes the form of a "quasi 2-functor" with values in a strict 2-category z Ham, defined as the "completion of a partial 2-category" Ham, notions which we define. Our construction extends Wehrheim and Woodward's Floer Field theory, and is inspired by Manolescu and Woodward's construction of symplectic instanton homology. It can be seen, in dimensions 1 `1, as a real analog of a construction by Moore and Tachikawa.Our construction is motivated by instanton gauge theory in dimensions 3 and 4: we expect to promote zHam to a (sort of) 3-category via equivariant Lagrangian Floer homology, and extend our quasi 2-functor to dimension 4, via equivariant analogues of Donaldson polynomials.

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A sheaf-theoretic model for SL(2,C) Floer homology

Cited by 8 publications

References 65 publications

Batalin--Vilkovisky quantization and supersymmetric twists

Batalin--Vilkovisky quantization and supersymmetric twists

A symplectic formula of generalized Casson invariants

A two-category of Hamiltonian manifolds, and a (1+1+1) field theory

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