Equivariant Gromov theory

The equivariant Gromov-Witten theory of P 1 Contents

Givental’s Lagrangian Cone and S-equivariant Gromov–witten Theory

In the approach to Gromov–Witten theory developed by Givental, genus-zero Gromov–Witten invariants of a manifold X are encoded by a Lagrangian cone in a certain infinite-dimensional symplectic vector space. We give a construction of this cone, in the spirit of S-equivariant Floer theory, in terms of S-equivariant Gromov–Witten theory of X × P. This gives a conceptual understanding of the “dilat...

Positivity Of Equivariant Gromov–Witten Invariants

We show that the equivariant Gromov-Witten invariants of a projective homogeneous space G/P exhibit Graham-positivity: when expressed as polynomials in the positive roots, they have nonnegative coefficients.

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...

Gromov-witten Theory Learning Seminar

Today, Jonathan spoke, delivering an overview of Gromov-Witten theory and how associativity of quantum cohomology leads to applications in enumerative geometry. Today we always work over C, and follow Fulton-Pandharipande’s notes [FP96]. Classically, if X is a nonsingular projective variety and β ∈ H2(X;Z), we want to know how many algebraic curves in X represent the class β. This relates to ve...