में बचाया:
| मुख्य लेखकों: | , |
|---|---|
| स्वरूप: | Preprint |
| प्रकाशित: |
2024
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/2412.09322 |
| टैग: |
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विषय - सूची:
- We introduce and study the notion of equivariant $\mathbb{Q}$-sliceness for strongly invertible knots. On the constructive side, we prove that every Klein amphichiral knot, which is a strongly invertible knot admitting a compatible negative amphichiral involution, is equivariant $\mathbb{Q}$-slice in a single $\mathbb{Q}$-homology $4$-ball, by refining Kawauchi's construction and generalizing Levine's uniqueness result. On the obstructive side, we show that the equivariant version of the classical Fox-Milnor condition, proved recently by the first author, also obstructs equivariant $\mathbb{Q}$-sliceness. We then introduce the equivariant $\mathbb{Q}$-concordance group and study the natural maps between concordance groups as an application. We also list some open problems for future study.