Symmetries and adjunction inequalities for knot Floer homology

Details Symmetries and adjunction inequalities for knot Floer homology Symmetries and adjunction inequalities for knot Floer homology

2010-12-14

arxiv.org/abs/1012.3088v2

Mathematics

Geometric Topology

32 pages, 10 figures; some results improved, adjunction inequality for cobordism maps added; overlaps with work of others dete

Scientific paper

We derive symmetries and adjunction inequalities of the knot Floer homology groups which appear to be especially interesting for homologically essential knots. Furthermore, we obtain an adjunction inequality for cobordism maps in knot Floer homologies. We demonstrate the adjunction inequalities and symmetries in explicit calculations which recover some of the main results from [1] on longitude Floer homology and also give rise to vanishing results on knot Floer homologies. Furthermore, using symmetries we prove that the knot Floer homology of a fiber distinguishes $\stwo\times\sone$ from other $\sone$-bundles over surfaces.

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