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$\mathbb{Z}_{2}$-equivariant Heegaard Floer cohomology of knots in $S^{3}$ as a strong Heegaard invariant. (arXiv:1810.01919v1 [math.GT])
来源于:arXiv
The $\mathbb{Z}_{2}$-equivariant Heegaard Floer cohomlogy
$\widehat{HF}_{\mathbb{Z}_{2}}(\Sigma(K))$ of a knot $K$ in $S^{3}$,
constructed by Hendricks, Lipshitz, and Sarkar, is an isotopy invariant which
is defined using bridge diagrams of $K$ drawn on a sphere. We prove that
$\widehat{HF}_{\mathbb{Z}_{2}}(\Sigma(K))$ can be computed from knot Heegaard
diagrams of $K$ and show that it is a strong Heegaard invariant. As a
topolocial application, we construct a transverse knot invariant
$\hat{\mathcal{T}}_{\mathbb{Z}_{2}}(K)$ as an element of
$\widehat{HFK}_{\mathbb{Z}_{2}}(\Sigma(K),K)$, which is a refinement of
$\widehat{HF}_{\mathbb{Z}_{2}}(\Sigma(K))$, and show that it is a refinement of
both the LOSS invariant $\hat{\mathcal{T}}(K)$ and the
$\mathbb{Z}_{2}$-equivariant contact class $c_{\mathbb{Z}_{2}}(\xi_{K})$. 查看全文>>