Grid homology for spatial graphs and a skein exact sequence
Zipei Zhuang
TL;DR
This paper introduces a grid homology theory for spatial graphs and extends the skein exact sequence from singular knots to this new framework, providing a novel algebraic tool for studying spatial graphs.
Contribution
The paper develops a grid homology theory specifically for spatial graphs and generalizes the skein exact sequence to this context, bridging knot theory and graph theory.
Findings
Established a grid homology framework for spatial graphs
Extended the skein exact sequence to spatial graphs
Provides new algebraic methods for analyzing spatial graphs
Abstract
We defined a grid homology theory for spatial graphs. We showed that the skein exact sequence of singular knots can be extended to our grid homology for spatial graphs.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research