English

Generalized Mazur Patterns and Immersed Heegaard Floer Homology

Geometric Topology 2024-10-15 v2

Abstract

Generalizing prior work of Levine, we give infinitely many examples of pattern knots P such that P(K) is not slice in any rational homology 4-ball, for any companion knot K. To show this, we establish a closed formula for the concordance invariants tau and epsilon of a family of satellite knots obtained from generalized Mazur patterns. Our main computational tool is the immersed curve technique from bordered Heegaard Floer homology arising from the work of Chen-Hanselman.

Keywords

Cite

@article{arxiv.2404.14578,
  title  = {Generalized Mazur Patterns and Immersed Heegaard Floer Homology},
  author = {Jay Patwardhan and Zheheng Xiao},
  journal= {arXiv preprint arXiv:2404.14578},
  year   = {2024}
}

Comments

51 pages, 46 figures; corrected a minor error in the proof of Proposition 4.1