Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Motivic Donaldson-Thomas invariants: summary of results

Maxim Kontsevich, Yan Soibelman

Abstract

This is a short summary of main results of our paper arXiv:0811.2435 where the concept of motivic Donaldson-Thomas invariant was introduced. It also contains a discussion of some open questions from the loc.cit., in particular, the geometry related to the split attractor flow.

Motivic Donaldson-Thomas invariants: summary of results

Abstract

This is a short summary of main results of our paper arXiv:0811.2435 where the concept of motivic Donaldson-Thomas invariant was introduced. It also contains a discussion of some open questions from the loc.cit., in particular, the geometry related to the split attractor flow.

Paper Structure

This paper contains 29 sections, 5 theorems, 115 equations.

Table of Contents

  1. Introduction
  2. Ind-constructible $3CY$-categories
  3. Ind-constructible triangulated $A_{\infty}$-categories, Calabi-Yau categories, stability conditions
  4. Motivic stack functions
  5. The motivic Milnor fiber
  6. Orientation data
  7. Motivic Hall algebra
  8. Quantum torus and motivic DT-invariants
  9. Motivic weights
  10. The motivic quantum torus
  11. From motivic Hall algebra to motivic quantum torus
  12. Quasi-classical limit and integrality
  13. Stability data on graded Lie algebras and wall-crossing formulas
  14. Stability data
  15. Wall-crossing formulas
  16. ...and 14 more sections

Key Result

Theorem 1

One has

Theorems & Definitions (22)

  • Definition 1
  • Remark 1
  • Definition 2
  • Theorem 1
  • Definition 3
  • Proposition 1
  • Definition 4
  • Theorem 2
  • Definition 5
  • Conjecture 1
  • ...and 12 more