Generalized Mazur Patterns and Immersed Heegaard Floer Homology

Jay Patwardhan; Zheheng Xiao

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arXiv · 2404.14578

Generalized Mazur Patterns and Immersed Heegaard Floer Homology

Jay Patwardhan·Zheheng Xiao

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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.

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Jay Patwardhan, Zheheng Xiao. 2024-04-22. Generalized Mazur Patterns and Immersed Heegaard Floer Homology. https://arxiv.org/abs/2404.14578

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