2021-05-18

Kristen Hendricks, Surgery formulas for involutive Heegaard Floer homology

Tags: #projects/notes/seminars #subjects/geomtop #subjects/geomtop/Floer-theory Refs: Heegard-Floer homology

Reference: Kristen Hendricks, Surgery formulas for involutive Heegaard Floer homology. Stanford Topology Seminar.

  • Want to study homology cobordism groups of 3-manifolds \(\Theta_{\mathbb{Z}}^3\).

    • We don’t understand the torsion in this group.
    • Reduce to study of a group of “\(\iota\) complexes”.
    • Theorem: it has a \({\mathbb{Z}}^{\infty}\) summand.
  • See Seifert fibered spaces.

  • People like HF because there are a lot of computational tools! In particular, a surgery formula.

22:01

Check out ideal sheaves, Birdgeland stability conditions.

  • “Rotate” an exact sequence to get an exact triangle :

    attachments/image_2021-05-18-22-20-05.png

    • Interpretation of the triangle: \(F = E \ominus {\mathcal{O}}(-n) = E \oplus {\mathcal{O}}(-n)[1]\).
    • Interpret \({\mathcal{O}}(-n)[1] = -{\mathcal{O}}(n)\).
  • What is an etale algebra?

#web/quick-notes #projects/notes/seminars #subjects/geomtop #subjects/geomtop/Floer-theory