On symmetries of peculiar modules; or, $\delta$-graded link Floer homology is mutation invariant

Abstract

We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant of 4-ended tangles which the author introduced in [arXiv:1712.05050]. In particular, we give an almost complete answer to the geography problem for components of peculiar modules of tangles. As a main application, we show that Conway mutation preserves the hat flavour of the relatively $\delta$-graded Heegaard Floer theory of links.

47 pages, many colour figures created with PSTricks and TikZ. Mathematica packages and notebooks are provided as ancillary files. v1: Comments welcome! v2: Restructured introduction and updated references. Submitted for peer-review

References in corpus (2)

• Mutation invariance of Khovanov homology over ${\mathbb{F}}_2$
• Heegaard Floer homology for manifolds with torus boundary: properties and examples

Cited by in corpus (4)

• Immersed curves in Khovanov homology
• Khovanov homology and strong inversions
• Thin links and Conway spheres
• A note on thickness of knots