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Lagrangian correspondences and pullbacks of virtual fundamental classes

Timo Schürg

Abstract

We argue that Lagrangian correspondences are the correct framework to study functoriality of virtual fundamental classes arising from a $-2$-symplectic derived structure.

Lagrangian correspondences and pullbacks of virtual fundamental classes

Abstract

We argue that Lagrangian correspondences are the correct framework to study functoriality of virtual fundamental classes arising from a -symplectic derived structure.

Paper Structure

This paper contains 7 sections, 6 theorems, 12 equations.

Table of Contents

  1. Introduction
  2. Related Works
  3. Overview
  4. Acknowledgements
  5. The virtual fundamental class of Oh-Thomas
  6. Lagrangian correspondences
  7. Virtual Pullbacks of Oh-Thomas-classes

Key Result

Theorem 3.12

Let$[(Y,\sigma)]^{\mathop{\mathrm{vir}}\nolimits}$ denote the virtual class represented by the quasi-smooth Lagrangian correspondece \begin{tikzcd}[cramped, sep=small] Y & \ar[l, "j"] N \ar[r] & \pt \end{tikzcd} in a symplectic oriented Borel-Moore homology theory $A_*$ with quasi-smooth

Theorems & Definitions (24)

  • Definition 3.1
  • Remark 3.2
  • Definition 3.3
  • Remark 3.4
  • Definition 3.5
  • Definition 3.6
  • Remark 3.7
  • Definition 3.8
  • Remark 3.9
  • Definition 3.10
  • ...and 14 more