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A configuration space approach to the chromatic polynomial, after Eastwood and Huggett
by
Yongwu Rong
George Washington University
This talks is motivated by two pieces of recent work, both realizing the chromatic polynomial of graphs using certain homology groups, but using very different approaches.
The first is a Khovanov type categorification for the chromatic polynomial, due to Laure Helme-Guizon and the speaker. This work will be presented at the same conference by L. Helme-Guizon.
The second, the main focus of this talk, is a generalized configuration space construction due to Eastwood and Huggett. They construct, for each positive integer k, and each each graph G, a topological space whose Euler characteristic is P_G(k) where P is the chromatic polynomial. Their construction is natural in the sense that the homology groups of the spaces satisfy a long exact sequence which yileds the well-known deletion-contraction rule.
We will present the work of Eastwood and Huggett and discuss some relations with our own approach.
Date received: November 14, 2004
Copyright © 2004 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # capf-14.