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

@article{Zibrowius2019OnSO, title={On symmetries of peculiar modules; or, \$\delta\$-graded link Floer homology is mutation invariant}, author={Claudius Zibrowius}, journal={arXiv: Geometric Topology}, year={2019} }

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.

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