A Refinement of the Spanning Surface Defect in $3$ and $4$ Dimensions
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914584161419264 |
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| author | Knihs, Julia Patel, Jeanette Sabloff, Joshua M. Rugg, Thea |
| author_facet | Knihs, Julia Patel, Jeanette Sabloff, Joshua M. Rugg, Thea |
| contents | The spanning surface defect uses spanning surfaces of a knot in the $3$-sphere to measure how far a knot is from being alternating. We refine the spanning surface defect and extend the definition to take into account surfaces in the $4$-ball. We use these extensions to make comparisons between the $3$- and $4$-dimensional settings, to reframe non-orientable slice-torus bounds on the non-orientable $4$-genus, and to prove a connected sum formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Refinement of the Spanning Surface Defect in $3$ and $4$ Dimensions Knihs, Julia Patel, Jeanette Sabloff, Joshua M. Rugg, Thea Geometric Topology 57K10 The spanning surface defect uses spanning surfaces of a knot in the $3$-sphere to measure how far a knot is from being alternating. We refine the spanning surface defect and extend the definition to take into account surfaces in the $4$-ball. We use these extensions to make comparisons between the $3$- and $4$-dimensional settings, to reframe non-orientable slice-torus bounds on the non-orientable $4$-genus, and to prove a connected sum formula. |
| title | A Refinement of the Spanning Surface Defect in $3$ and $4$ Dimensions |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2602.13186 |