Stabilization of 4-manifolds

Cho, Yong-Seung

doi:10.1007/s11425-014-4778-2

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…Darboux's Theorem 2.1 ( [6]). Every symplectic form ω on M is locally diffeomorphic to the standard form ω 0 on R 2n .…”

Section: Symplectic Manifoldsmentioning

confidence: 99%

“…In Section 3.1, we study ϕ-coholomorphic map, moduli space of ϕ-coholomorphic maps which represent a homology class of dimension two, Gromov-Witten type cohomology, quantum type product and quantum type cohomology, Gromov-Witten type potentials on the product of a symplectic manifold, and an almost contact metric manifold [5,6,13]. In Section 3.2, we investigate the symplectic type action functional on the universal covering space of the contractible loops, its gradient flow line, the moduli space of the connecting flow orbits between critical loops, Floer type cochain complex, and Floer type cohomology with coefficients in a Novikov ring [7,9,13].…”

Section: Introductionmentioning

confidence: 99%

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Symplectic Manifolds: Gromov-Witten Invariants on Symplectic and Almost Contact Metric Manifolds

Cho¹

2017

Manifolds - Current Research Areas

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In this chapter, we introduce Gromov-Witten invariant, quantum cohomology, GromovWitten potential, and Floer cohomology on symplectic manifolds, and in connection with these, we describe Gromov-Witten type invariant, quantum type cohomology, Gromov-Witten type potential and Floer type cohomology on almost contact metric manifolds. On the product of a symplectic manifold and an almost contact metric manifold, we induce some relations between Gromov-Witten type invariant and quantum cohomology and quantum type invariant. We show that the quantum type cohomology is isomorphic to the Floer type cohomology.

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“…Darboux's Theorem 2.1 ( [6]). Every symplectic form ω on M is locally diffeomorphic to the standard form ω 0 on R 2n .…”

Section: Symplectic Manifoldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symplectic Manifolds: Gromov-Witten Invariants on Symplectic and Almost Contact Metric Manifolds

Cho¹

2017

Manifolds - Current Research Areas

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Gromov–Witten Invariants on the Products of Almost Contact Metric Manifolds

Cho¹

2017

Springer Proceedings in Mathematics &Amp; Statistics

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Floer type cohomology on cosymplectic manifolds

Cho

Chai

2015

Int. J. Geom. Methods Mod. Phys.

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We investigate a Floer type cohomology on cosymplectic manifolds M. To do this, we study a symplectic type action functional on the universal covering space of the loop space of contractible loops in M and the moduli space of gradient flow lines of the functional. The cochain complex induced by the critical points of the functional produces Floer type cohomology of M which is naturally isomorphic to a quantum type cohomology of M. We have an Arnold type theorem for Hamiltonian cosymplectomorphisms on compact semipositive cosymplectic manifolds. As an example, we consider the product of a Calabi–Yau 3-fold and the unit circle.

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Stabilization of 4-manifolds

Cited by 4 publications

References 15 publications

Symplectic Manifolds: Gromov-Witten Invariants on Symplectic and Almost Contact Metric Manifolds

Symplectic Manifolds: Gromov-Witten Invariants on Symplectic and Almost Contact Metric Manifolds

Gromov–Witten Invariants on the Products of Almost Contact Metric Manifolds

Floer type cohomology on cosymplectic manifolds

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