graph homology
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2018 ◽  
Vol 27 (03) ◽  
pp. 1840007
Author(s):  
Radmila Sazdanovic ◽  
Daniel Scofield

Khovanov homology of a link and chromatic graph homology are known to be isomorphic in a range of homological gradings that depend on the girth of a graph. We discuss patterns shared by these two homology theories. In particular, we improve the bounds for the homological span of chromatic homology by Helme–Guizon, Przytycki and Rong. An explicit formula for the rank of the third chromatic homology group on the main diagonal is given and used to compute the corresponding Khovanov homology group and the fourth coefficient of the Jones polynomial for links with certain diagrams.


2016 ◽  
Vol 76 (3) ◽  
pp. 1126-1151 ◽  
Author(s):  
Jared C. Bronski ◽  
Lee DeVille ◽  
Timothy Ferguson

2014 ◽  
Vol 176 (1) ◽  
pp. 345-374 ◽  
Author(s):  
James Conant ◽  
Martin Kassabov ◽  
Karen Vogtmann
Keyword(s):  

2013 ◽  
Vol 336 ◽  
pp. 180-222 ◽  
Author(s):  
Dirk Kreimer ◽  
Matthias Sars ◽  
Walter D. van Suijlekom

2012 ◽  
Vol 7 (2) ◽  
pp. 223-235 ◽  
Author(s):  
Vladimir Baranovsky ◽  
Radmila Sazdanovic

2012 ◽  
Vol 11 (02) ◽  
pp. 1250031
Author(s):  
PAUL TURNER ◽  
EMMANUEL WAGNER

Przytycki has established a connection between the Hochschild homology of an algebra A and the chromatic graph homology of a polygon graph with coefficients in A. In general the chromatic graph homology is not defined in the case where the coefficient ring is a non-commutative algebra. In this paper we define a new homology theory for directed graphs which takes coefficients in an arbitrary A–A bimodule, for A possibly non-commutative, which on polygons agrees with Hochschild homology through a range of dimensions.


2011 ◽  
Vol 22 (11) ◽  
pp. 1545-1559
Author(s):  
ATSUSHI ISHII

We give a framework to normalize a regular isotopy invariant of a spatial graph, and introduce many normalizations satisfying the same relation under a local move. We normalize the Yamada polynomial for spatial embeddings of almost all trivalent graphs without a bridge, and see the benefit to utilize our normalizations from the viewpoint of skein relations, the finite type invariants, and evaluations of the Yamada polynomial. We show that the collection of the differences between two of our normalizations is a complete spatial-graph-homology invariant.


2008 ◽  
Vol 17 (12) ◽  
pp. 1549-1559 ◽  
Author(s):  
E. WAGNER

In analogy with a recursive formula for the HOMFLY-PT polynomial of links given by Jaeger, we give a recursive formula for the graph polynomial introduced by Kauffman and Vogel. We show how this formula extends to the Khovanov–Rozansky graph homology.


2008 ◽  
Vol 218 (6) ◽  
pp. 1878-1894 ◽  
Author(s):  
A. Lazarev ◽  
A.A. Voronov
Keyword(s):  

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