Kristen Hendricks, Surgery formulas for involutive Heegaard Floer homology
Tags: #projects/notes/seminars #geomtop #geomtop/Floer-theory Refs: Heegard-Floer homology
Reference: Kristen Hendricks, Surgery formulas for involutive Heegaard Floer homology. Stanford Topology Seminar.
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Want to study homology cobordism groups of 3-manifolds \(\Theta_{\mathbf{Z}}^3\).
- We don’t understand the torsion in this group.
- Reduce to study of a group of “\(\iota\) complexes”.
- Theorem: it has a \({\mathbf{Z}}^{\infty}\) summand.
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See Seifert fibered spaces.
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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.
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“Rotate” an exact sequence to get an exact triangle :
- Interpretation of the triangle: \(F = E \ominus {\mathcal{O}}(-n) = E \oplus {\mathcal{O}}(-n)[1]\).
- Interpret \({\mathcal{O}}(-n)[1] = -{\mathcal{O}}(n)\).
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What is an etale algebra?