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 |
On the first group of A3 cohomology of graphs
by
Milena Pabiniak
George Washington University
Coauthors: Jozef H. Przytycki, Radmila Sazdanovic
We are analyzing properties of the first group of
A3 graph cohomology. We concentrate on the grading implied by
the interpretation of Hochschild homology as graph homology of a
polygon, that is (1, 2v-3).
We work with homology because this approach enables us
to establish straightforward
connections to the
homology of simplicial complexes built on our graph.
Precisely, the group H0, 2v-3A3(G) can be almost entirely
recovered from homology of two cell complexes with graph G as
1-skeleton:
- X3, 4(G) obtained from G
by adding 2-cells along 3-cycles and 4-cycles of G,
-
X(3), 4(G) obtained from G by adding 2-cells along
4-cycles of G and by identifying edges of every 3-cycle in
G in a coherent way.
Computing homology of those chain complexes is related to calculating
homology H0, 2v-3A3(G) with coefficients in Z3
and
Z [1/3] (this is localization on the multiplicative
set generated by 3). Information we obtain in this way is not
complete as we cannot distinguish Z3i-
torsion for an arbitrary i.
In some special cases we will be able to find this lacking piece of information by
computing
3H0, 2v-3A3(G).
In particular we proved that
for complete graph Kn with n vertices, n ≥ 4:
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H1, 2n-3A3(Kn) = Z2 + Z3n-1 + Z[(n(n-1)(2n-7))/6]. |
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Date received: May 3, 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-17.