Kirby-Thompson invariants of distant sums of standard surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911874340093952 |
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| author | Taniguchi, Minami |
| author_facet | Taniguchi, Minami |
| contents | Blair, Campisi, Taylor, and Tomova defined the L-invariant L(F) of a knotted surface F, using pants complexes of trisection surfaces of bridge trisections of F. After that, Aranda, Pongtanapaisan, and Zhang introduced the L*-invariant L*(F) using dual curve complexes instead of pants complexes. In this paper, we determine both of L-invariant and L*-invariant of any finite distant sum of standard surfaces, and this is the first example of knotted surfaces whose bridge numbers and these invariants can be arbitrary large. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06976 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kirby-Thompson invariants of distant sums of standard surfaces Taniguchi, Minami Geometric Topology Primary 57K10, Secondary 57K20 Blair, Campisi, Taylor, and Tomova defined the L-invariant L(F) of a knotted surface F, using pants complexes of trisection surfaces of bridge trisections of F. After that, Aranda, Pongtanapaisan, and Zhang introduced the L*-invariant L*(F) using dual curve complexes instead of pants complexes. In this paper, we determine both of L-invariant and L*-invariant of any finite distant sum of standard surfaces, and this is the first example of knotted surfaces whose bridge numbers and these invariants can be arbitrary large. |
| title | Kirby-Thompson invariants of distant sums of standard surfaces |
| topic | Geometric Topology Primary 57K10, Secondary 57K20 |
| url | https://arxiv.org/abs/2405.06976 |