Invariance of Knot Lattice Homology and Homotopy

<p>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 nested singularity type. </p>

Author dc:creator

• Niemi-Colvin, Seppo Matthew

Advisor dc:contributor.advisor

• Levine, Adam

• Mathematics
• knot Floer homology
• knot theory
• singularity theory

Handle dc:identifier.uri

https://hdl.handle.net/10161/25199

OAI identifier oai:identifier

oai:dukespace.lib.duke.edu:10161/25199