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Heegaard Floer invariants for cyclic 3-orbifolds

Saibal Ganguli, Mainak Poddar

Abstract

We define a notion of Heegaard Floer homology for three dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected.

Heegaard Floer invariants for cyclic 3-orbifolds

Abstract

We define a notion of Heegaard Floer homology for three dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected.
Paper Structure (10 sections, 4 theorems, 46 equations, 6 figures)

This paper contains 10 sections, 4 theorems, 46 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Bordered Floer Homology
  3. $A$ and $D$ structures
  4. Bordered three manifolds
  5. Orbifold Heegard Floer for one component knot singularity
  6. Definition
  7. Orbifold Heegaard Floer for two component singular locus
  8. More $A$ structures
  9. $DA$ structures and invariance
  10. Multiple component singular locus

Key Result

Lemma 4.1

The operators $\overline{m}_k$ statisfy the the structural equations compat of an $A$ structure.

Figures (6)

  • Figure 1: Quiver related to the path algebra $\mathcal{A}$
  • Figure 2: Pointed matched circle $\mathcal{Z}$
  • Figure 3: A genus $1$ bordered Heegaard diagram
  • Figure 4: Type $D$ structure for $(D^2 \times S^1, \psi)$
  • Figure 5: The structure $D_N$
  • ...and 1 more figures

Theorems & Definitions (13)

  • Remark 3.1
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • proof
  • Definition 4.1
  • Theorem 4.3
  • proof
  • Remark 4.4
  • Lemma 4.5
  • ...and 3 more