• Corpus ID: 202542567

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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References

SHOWING 1-10 OF 23 REFERENCES
Heegaard Floer homology for manifolds with torus boundary: properties and examples
This is a companion paper to earlier work of the authors, which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured torus. We prove a
Peculiar modules for 4‐ended tangles
With a 4‐ended tangle T , we associate a Heegaard Floer invariant CFT∂(T) , the peculiar module of T . Based on Zarev's bordered sutured Heegaard Floer theory (Zarev, PhD Thesis, Columbia University,
On a polynomial Alexander invariant for tangles and its categorification
We generalise the Kauffman state formula for the classical multivariate Alexander polynomial of knots and links to tangles and thereby obtain a finite set of polynomial tangle invariants. In the
Heegaard Floer homology as morphism spaces
In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present
Holomorphic discs and sutured manifolds
In this paper we construct a Floer-homology invariant for a natural and wide class of sutured manifolds that we call balanced. This generalizes the Heegaard Floer hat theory of closed three-manifolds
Twisting, mutation and knot Floer homology
Let $\mathcal{L}$ be a knot with a fixed positive crossing and $\mathcal{L}_n$ the link obtained by replacing this crossing with $n$ positive twists. We prove that the knot Floer homology
Bordered Floer homology for manifolds with torus boundary via immersed curves
This paper gives a geometric interpretation of bordered Heegaard Floer homology for manifolds with torus boundary. If $M$ is such a manifold, we show that the type D structure
MUTATION INVARIANCE OF KHOVANOV HOMOLOGY OVER F2
We prove that Khovanov homology and Lee homology with coefficients in F2 = Z/2Z are invariant under component-preserving link mutations.
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