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

Claudius Zibrowius

doi:10.4171/jems/1201

JournalsjemsVol. 25, No. 8pp. 2949–3006

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

Claudius Zibrowius
Universität Regensburg, Germany

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

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Abstract

We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant of 4-ended tangles which the author introduced in [J. Topol. 13 (2020)]. 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 $δ$ -graded Heegaard Floer theory of links.

Cite this article

Claudius Zibrowius, On symmetries of peculiar modules, or $δ$ -graded link Floer homology is mutation invariant. J. Eur. Math. Soc. 25 (2023), no. 8, pp. 2949–3006

DOI 10.4171/JEMS/1201