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 -graded Heegaard Floer theory of links.
Cite this article
Claudius Zibrowius, On symmetries of peculiar modules, or -graded link Floer homology is mutation invariant. J. Eur. Math. Soc. 25 (2023), no. 8, pp. 2949–3006DOI 10.4171/JEMS/1201