论文标题
打结晶格同源性和同喻的自然性和自然性
Invariance and naturality of knot lattice homology and homotopy
论文作者
论文摘要
奇异性和广义代数链接的链接是从潜在的奇异复杂代数表面和它们内部复杂曲线中构建三个manifolds和平滑链接的方式。我们证明，打结晶格同源性是理性同源性球体中普通代数结的平滑结型的不变性。在这种情况下，打结晶格同源性可以实现为双过滤波器类型的细胞同源性，该类型本身就是不变的。一路上，我们表明，广义代数链路的拓扑链接类型决定了用于创建它的嵌套奇点类型的最小管道分辨率的拓扑。打结晶格同喻是自然不变的，因为结的差异性与最小的良好分辨率相当地发挥作用将提供与任何演示相关的双重过滤结晶格空间之间的合理空间。
Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice homology is an invariant of the smooth knot type of a generalized algebraic knot in a rational homology sphere. In that case, knot lattice homology can be realized as the cellular homology of a doubly-filtered homotopy type, which is itself invariant. Along the way, we show that the topological link type of a generalized algebraic link determines the topology of the minimal plumbing resolution for the nested singularity type used to create it. Knot lattice homotopy is a natural invariant in that diffeomorphisms of the knot that play suitably well with the minimal good resolution will provide a contractible space of morphisms between the doubly-filtered knot lattice spaces associated to any presentation.
