On the tau invariants in instanton and monopole Floer theories
| Autor: | Ghosh, Sudipta, Li, Zhenkun, Wong, C. -M. Michael |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We unify two existing approaches to the tau invariants in instanton and monopole Floer theories, by identifying $\tau_{\mathrm{G}}$, defined by the second author via the minus flavors $\underline{\operatorname{KHI}}^-$ and $\underline{\operatorname{KHM}}^-$ of the knot homologies, with $\tau_{\mathrm{G}}^{\sharp}$, defined by Baldwin and Sivek via cobordism maps of the $3$-manifold homologies induced by knot surgeries. We exhibit several consequences, including a relationship with Heegaard Floer theory, and use our result to compute $\underline{\operatorname{KHI}}^-$ and $\underline{\operatorname{KHM}}^-$ for twist knots. Comment: 44 pages, 13 figures. Major revision with improved exposition and expanded introduction |
| Databáze: | arXiv |
| Externí odkaz: |
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