TL;DR
This paper introduces a generalized concept called virtual pull-backs for DM-type morphisms of stacks with perfect obstruction theories, proving their functoriality and applying them to Gromov-Witten invariants of blow-ups and projective bundles.
Contribution
It generalizes Gysin maps to a broader class of morphisms using virtual pull-backs and establishes their functorial properties.
Findings
Virtual pull-backs extend Gysin maps to DM stacks.
Proved functoriality of virtual pull-backs.
Applied to Gromov-Witten invariants of blow-ups and projective bundles.
Abstract
We propose a generalization of Gysin maps for DM-type morphisms of stacks that admit a perfect relative obstruction theory , which we call a "virtual pull-back". We prove functoriality properties of virtual pull-backs. As applications, we analyze Gromov-Witten invariants of blow-ups and projective bundles.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory