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Examples of relative quantum cohomology

Kai Hugtenburg, Sara B. Tukachinsky

Abstract

We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.

Examples of relative quantum cohomology

Abstract

We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.
Paper Structure (50 sections, 68 theorems, 230 equations, 4 tables)

This paper contains 50 sections, 68 theorems, 230 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Acknowledgments
  3. Background
  4. Setting and notation
  5. Bases
  6. Rings
  7. Closed GW
  8. Open GW
  9. Interplay
  10. Sign changes of the open GW
  11. Closed quantum cohomology
  12. Relative quantum cohomology
  13. Big closed quantum cohomology
  14. Big relative quantum cohomology
  15. Complete intersections
  16. ...and 35 more sections

Key Result

Theorem 1

If $[L]\ne 0$, then the relative quantum cohomology is given by The relative quantum cohomology injects into the absolute one via

Theorems & Definitions (122)

  • Theorem 1
  • Remark 1.1
  • Theorem 2
  • Theorem 3
  • Remark 1.2
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Proposition 1.3
  • ...and 112 more