The minimal Rickard complexes of braids on two strands
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908979056082944 |
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| author | Wang, Joshua |
| author_facet | Wang, Joshua |
| contents | The Rickard complex of a braid with strands colored by positive integers is a chain complex of singular Soergel bimodules. The complex determines the colored triply-graded homology and colored sl(N) homology of the braid closure, when closure is color-compatible. For each braid on two strands with any colors, we construct a minimal complex that is homotopy equivalent to its Rickard complex. It is not obtained by laborious simplification; instead, it is defined directly by explicit formulas obtained by educated guesswork and reverse engineering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The minimal Rickard complexes of braids on two strands Wang, Joshua Geometric Topology Quantum Algebra The Rickard complex of a braid with strands colored by positive integers is a chain complex of singular Soergel bimodules. The complex determines the colored triply-graded homology and colored sl(N) homology of the braid closure, when closure is color-compatible. For each braid on two strands with any colors, we construct a minimal complex that is homotopy equivalent to its Rickard complex. It is not obtained by laborious simplification; instead, it is defined directly by explicit formulas obtained by educated guesswork and reverse engineering. |
| title | The minimal Rickard complexes of braids on two strands |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2510.13764 |