Hamiltonian handleslides for Heegaard Floer homology

By Timothy Perutz. 2008

53 citations recorded by the source corpus.

A $g$-tuple of disjoint, linearly independent circles in a Riemann surface of genus $g$ determines a `Heegaard torus' in its $g$-fold symmetric product. Changing the circles by a handleslide produces a new torus. It is proved that, for symplectic forms with certain properties, these two tori are Hamiltonian-isotopic Lagrangian submanifolds. This provides an alternative route to the handleslide-invariance of Ozsvath-Szabo's Heegaard Floer homology.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b5ebc21cb80ad88fed54c09f8518ca46fdfa3e8e

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Citations in the corpus

A survey of Heegaard Floer homology (2013, background): “Perutz [82] constructed a symplectic structure on SympΣq compatible with the complex structure that makes Tα and Tβ Lagrangian and monotonic with minimal Maslov number two.”
The decategorification of sutured Floer homology (2009, background): “By [32], both isotopies and handleslides correspond to isotopies of Tα and Tβ inside Sym(Σ).”
Localization for Involutions in Floer Cohomology (2010, background): “Perutz ([21], building on results of Varouchas [30]) provided a direct construction of Kähler forms on symmetric products, which we will now adapt to our purpose.”
Fukaya categories and bordered Heegaard-Floer homology (2010, background): “(This is an easy consequence of the main result in [11]).”
Fukaya categories of symmetric products and bordered Heegaard-Floer homology (2010, background): “disjoint closed curves; the arc slide operation then becomes a handle slide and the result of [12] applies.”
Asymptotically cylindrical Calabi-Yau manifolds (2012, methodology): “We now apply the (elementary but clever) Varouchas method [45] for smoothing singular Kähler forms with continuous local potentials; the presentation in Perutz [40] is particularly convenient.”
AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “(In fact, one can equip Sym d (Σ) with a symplectic form, such that T α and T β are Lagrangian; see [Per08].)”