Towards quantum cohomology of real varieties
Ozgur Ceyhan
TL;DR
This paper explores the quantum cohomology of real algebraic varieties through Gromov-Witten-Welschinger classes, proposing a DG-operad framework and discussing potential mirror symmetry implications.
Contribution
It introduces a DG-operad formulation of quantum cohomology for real varieties using GWW-classes and revisits Horava's definition with new mathematical tools.
Findings
Reformulation of quantum cohomology as a DG-operad
Application of GWW-classes to real algebraic varieties
Speculation on mirror symmetry for real varieties
Abstract
This paper is devoted to a discussion of Gromov-Witten-Welschinger (GWW) classes and their applications. In particular, Horava's definition of quantum cohomology of real algebraic varieties is revisited by using GWW-classes and it is introduced as a DG-operad. In light of this definition, we speculate about mirror symmetry for real varieties.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology