Unoriented knot Floer homology and the unoriented four-ball genus

By Peter S. Ozsv'ath, A. Stipsicz, Zolt'an Szab'o. 2015

47 citations recorded by the source corpus.

In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying the construction of knot Floer homology HFK-minus. The resulting groups were then used to define concordance homomorphisms indexed by t in [0,2]. In the present work we elaborate on the special case t=1, and call the corresponding modified knot Floer homology the unoriented knot Floer homology. Using elementary methods (based on grid diagrams and normal forms for surface cobordisms), we show that the resulting concordance homomorphism gives a lower bound for the smooth 4-dimensional crosscap number of a knot K --- the minimal first Betti number of a smooth (possibly non-orientable) surface in the 4-disk that meets the boundary 3-sphere along the given knot K.

Subfields: Geometry and Topology, Neurology

View Paper: https://www.semanticscholar.org/paper/3deeaba7363f6ed4fc62ef203a411c1a7afcb0e9

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In Geometry and Topology

  1. A. Stipsicz
  2. Peter S. Ozsv'ath
  3. Zolt'an Szab'o
  4. Ciprian Manolescu
  5. P. Lisca
  6. Jacob Rasmussen
  7. John A. Baldwin
  8. M. Hedden

In Neurology

  1. A. Stipsicz
  2. Peter S. Ozsv'ath
  3. Zolt'an Szab'o
  4. M. Hedden
  5. Ian Zemke
  6. Ciprian Manolescu
  7. Jacob Rasmussen
  8. John A. Baldwin

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