A minimality property for knots without Khovanov 2-torsion
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912686979153920 |
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| author | Gujral, Onkar Singh Wang, Joshua |
| author_facet | Gujral, Onkar Singh Wang, Joshua |
| contents | A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology. We show that if a knot $K$ has no 2-torsion in its Khovanov homology, then the rank of its reduced Khovanov homology is minimal among all knots obtainable from $K$ by a proper rational tangle replacement. It follows, for example, that unknotting number 1 knots have 2-torsion in their Khovanov homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06163 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A minimality property for knots without Khovanov 2-torsion Gujral, Onkar Singh Wang, Joshua Geometric Topology Quantum Algebra A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology. We show that if a knot $K$ has no 2-torsion in its Khovanov homology, then the rank of its reduced Khovanov homology is minimal among all knots obtainable from $K$ by a proper rational tangle replacement. It follows, for example, that unknotting number 1 knots have 2-torsion in their Khovanov homology. |
| title | A minimality property for knots without Khovanov 2-torsion |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2310.06163 |