Towards Quantum Cohomology of Real Varieties

Ceyhan, Ozgur

doi:10.1007/978-0-8176-4831-2_4

Cited by 2 publications

(1 citation statement)

References 33 publications

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“…In this section, we discuss two possible geometric constructions of algebras over the planar operad P. The first one follows closely the approach of Cohen and Godin's in constructing string topology operations [4]. The second one is in the spirit of Gromov-Witten theory [10], in the real algebraic geometry setting (see for instance [3]).…”

Section: Algebras Over Planar Operadmentioning

confidence: 99%

Open string theory and planar algebras

Ceyhan¹,

Marcolli²

2010

J. Phys. A: Math. Theor.

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In this paper, we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the wellknown relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry and subfactors of von Neumann algebras.

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Section: Algebras Over Planar Operadmentioning

confidence: 99%

Open string theory and planar algebras

Ceyhan¹,

Marcolli²

2010

J. Phys. A: Math. Theor.

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Graph homology of the moduli space of pointed real curves of genus zero

Ceyhan

2007

Sel. math., New ser.

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The moduli space M σ S (R) parameterizes the isomorphism classes of S-pointed stable real curves of genus zero which are invariant under relabeling by the involution σ. This moduli space is stratified according to the degeneration types of σ-invariant curves. The degeneration types of σ-invariant curves are encoded by their dual trees with additional decorations. We construct a combinatorial graph complex generated by the fundamental classes of strata of M σ S (R). We show that the homology of M σ S (R) is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of M σ S (R).

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Towards Quantum Cohomology of Real Varieties

Cited by 2 publications

References 33 publications

Open string theory and planar algebras

Open string theory and planar algebras

Graph homology of the moduli space of pointed real curves of genus zero

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