AI 中文总结
为强可逆纽结开发等变网格同调，引入编码强反转的对称网格图，证明定理，研究对合映射锥，定义相关不变量并证明其性质。
AI 中文摘要
我们为强可逆纽结发展了网格同调的等变版本。我们引入编码强反转的对称网格图，证明每个强可逆纽结都有这样的表示，并建立了相应的克伦威尔定理类似物。一个对称网格在相关网格复形上诱导一个对合。我们研究恒等映射与这个对合之和的映射锥，证明其同调是强可逆纽结的不变量。最后，我们定义了τ不变量和勒让德网格不变量的等变类似物，并表明前者为等变解结数和简单等变协边的亏格提供下界。
英文摘要
We study an equivariant version of grid homology for strongly invertible knots. We consider symmetric grid diagrams encoding the strong inversion, prove that every strongly invertible knot admits such a representation, and establish the corresponding analogue of Cromwell's theorem. A symmetric grid induces an involution on the associated grid complex. We study the mapping cone of the sum of the identity and this involution, proving that its homology is an invariant of strongly invertible knots. Finally, we define equivariant analogues of the tau invariant and of the Legendrian grid invariants, and show that the former provide lower bounds for equivariant unknotting numbers and for the genus of simple equivariant cobordisms.
Comments62 pages, 26 figures. v2 Minor revisions. Comments are welcome!
