Topology Atlas | Conferences
Knots in Washington XXII
May 5-7, 2006
George Washington University
Washington, DC, USA |
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Organizers Jozef H. Przytycki (GWU), przytyck@gwu.edu, Yongwu Rong (GWU), rong@gwu.edu, Alexander Shumakovitch (GWU), shurik@gwu.edu
Conference Homepage |
Torsion in the first group of the chromatic graph cohomology over algebras Z[x]/(xm)
by
Radmila Sazdanovic
George Washington University
Coauthors: Jozef H. Przytycki, Milena Pabiniak
In this talk we focus on the first chromatic graph cohomology over algebra Z[x]/(xm) of truncated polynomials.
In particular, we are interested in grading motivated by the interpretation of Hochschild homology as graph
cohomology of polygons and its generalization to arbitrary graphs.
As an introduction to this talk, my coauthors will give the complete description of H1, v-1A2(G) and
H1, 2v-3A3(G). However, for Z[x]/(xm) and m > 3 we give
only conjectures based both on theory developed for m=2, 3 and computational results.
Theorem 1.
For complete graph with n vertices Kn, n ≥ 4 have
H1, 2n-3A3(Kn) = Z2⊕Z3n-1⊕Z[(n(n-1)(2n-7))/6]. |
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Corollary 2.
If a graph G contains a triangle then H1, 2v(G)-3A3(G)
contains Z3 torsion.
We show that (∀n) (∃ simple G) Zn ∈ torH1, 2v-3A3(G).
Conjecture 3.
For any graph Wn with n vertices where one vertex is of degree n-1 and
all the rest are of degree 3 (wheel), n > 4 and m ≥ 4 the
following holds:
H1, 4n-3Am(Wnout)=Zmn-1 ⊕Zn-2 |
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H1, 4n-3Am(Wnin)=Zmn-2⊕Zn-2 |
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Conjecture 4.
For complete graph Kn where n ≥ 4 and odd m > 3 the following is true:
H1, (m-1)(n-2)+1Am(Kn) = Zm[(n (n-1)(n-2))/6] ⊕Z2[(n (n-1)(n-2)(n-3))/24] ⊕Z[(n (n-1)(n-2)(n-3))/12] |
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Moreover, we will present some computational results for width of
H1A3(G) of several families of graphs graphs.
Date received: May 4, 2006
Copyright © 2006 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 # casv-18.