Generalized Mazur Patterns and Immersed Heegaard Floer Homology
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910647493591040 |
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| author | Patwardhan, Jay Xiao, Zheheng |
| author_facet | Patwardhan, Jay Xiao, Zheheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Mazur Patterns and Immersed Heegaard Floer Homology Patwardhan, Jay Xiao, Zheheng Geometric Topology 57K18, 57K10 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. |
| title | Generalized Mazur Patterns and Immersed Heegaard Floer Homology |
| topic | Geometric Topology 57K18, 57K10 |
| url | https://arxiv.org/abs/2404.14578 |