Equivariant algebraic concordance of strongly invertible knots
| Autor: | Di Prisa, Alessio |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | By considering a particular type of invariant Seifert surfaces we define a homomorphism $\Phi$ from the (topological) equivariant concordance group of directed strongly invertible knots $\widetilde{\mathcal{C}}$ to a new equivariant algebraic concordance group $\widetilde{\mathcal{G}}^{\mathbb{Z}}$. We prove that $\Phi$ lifts both Miller and Powell's equivariant algebraic concordance homomorphism, and Alfieri and Boyle's equivariant signature. Moreover, we provide a partial result on the isomorphism type of $\widetilde{\mathcal{G}}^{\mathbb{Z}}$, and we obtain a new obstruction to equivariant sliceness, which can be viewed as an equivariant Fox-Milnor condition. We define new equivariant signatures and using these we obtain novel lower bounds on the equivariant slice genus. Finally, we show that $\Phi$ can obstruct equivariant sliceness for knots with Alexander polynomial one. Comment: 43 pages, 8 figures, 1 table. The paper has been accepted for publication by the Journal of Topology |
| Databáze: | arXiv |
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