Differentials on Graph Complexes III - Deleting a Vertex
Marko \v{Z}ivkovi\'c

TL;DR
This paper introduces a new differential called deleting a vertex in hairy graph complexes, demonstrating its near-acyclicity and enabling the construction of cohomology classes via the waterfall mechanism.
Contribution
It presents a novel differential in hairy graph complexes and proves its near-acyclicity, facilitating new methods for constructing graph cohomology classes.
Findings
Hairy graph complex with the new differential is almost acyclic
The waterfall mechanism for cohomology class construction is justified
Potential for further applications of the deleting a vertex differential
Abstract
We prove that the hairy graph complex with the extra differential is almost acyclic. This justifies the construction of hairy graph cohomology classes by the waterfall mechanism. The main idea used in the paper is a new differential, deleting a vertex. We hope that the new differential can have further applications in the study of graph cohomology.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis
