On Infinite Cycles in Graphs: Or How to Make Graph Homology Interesting

2004 ◽  
Vol 111 (7) ◽  
pp. 559 ◽  
Author(s):  
Reinhard Diestel
Keyword(s):  
Graph Homology ◽  
Infinite Cycles

scholarly journals Matroid and Tutte-Connectivity in Infinite Graphs

10.37236/2832 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Henning Bruhn
Keyword(s):  
Infinite Graph ◽  
Infinite Graphs ◽  
Dual Graphs ◽  
Connectivity Function ◽  
Cycle Matroid ◽  
Infinite Cycles

We relate matroid connectivity to Tutte-connectivity in an infinite graph. Moreover, we show that the two cycle matroids, the finite-cycle matroid and the cycle matroid, in which also infinite cycles are taken into account, have the same connectivity function. As an application we re-prove that, also for infinite graphs, Tutte-connectivity is invariant under taking dual graphs.

scholarly journals A note on free products with a normal amalgamation

1968 ◽  
Vol 8 (3) ◽  
pp. 631-637 ◽  
Author(s):  
R. A. Bryce
Keyword(s):  
Free Products ◽  
One To One ◽  
Image Position ◽  
Subgroup Theorem ◽  
Infinite Cycles

It is a consequence of the Kurosh subgroup theorem for free products that if a group has two decompositions where each Ai and each Bj is indecomposable, then I and J can be placed in one-to-one correspondence so that corresponding groups if not conjugate are infinite cycles. We prove here a corresponding result for free products with a normal amalgamation.

The MOD 2 K-Homology of Ω3S3X

1988 ◽  
Vol 40 (1) ◽  
pp. 142-196 ◽  
Author(s):  
J. G. Mayorquin
Keyword(s):  
Spectral Sequence ◽  
Cyclic Group ◽  
Image Position ◽  
Torsion Free ◽  
Infinite Cycles

In order to compute the group K*(Ω3S3X; Z/2) when X is a finite, torsion free CW-complex we apply the techniques developed by Snaith in [38], [39], [40], [41] which were used in [42] to determine the Atiyah-Hirzebruch spectral sequence ( [11], [1, Part III])for X as above. Roughly speaking the method consists in defining certain classes in K*(Ω3S3X; Z/2) via the π-equivariant mod 2 K-homology of S2 × Y2,([35]), π the cyclic group of order 2 (acting antipodally on S2, by permuting factors in Y2, and diagonally on S2 × Y2), Y a finite subcomplex of Ω3S3X, and then showing that the classes so produced map under the edge homomorphism to cycles (in the E1-term of the Atiyah-Hirzebruch spectral sequence forwhich determine certain homology classes of H*(Ω3S3X; Z/2), thus exhibiting these as infinite cycles of the spectral sequence

scholarly journals Spatial Random Permutations and Infinite Cycles

2008 ◽  
Vol 285 (2) ◽  
pp. 469-501 ◽  
Author(s):  
Volker Betz ◽  
Daniel Ueltschi
Keyword(s):  
Random Permutations ◽  
Infinite Cycles

scholarly journals Torsion in graph homology

2006 ◽  
Vol 190 ◽  
pp. 139-177 ◽  
Author(s):  
Laure Helme-Guizon ◽  
Józef H. Przytycki ◽  
Yongwu Rong
Keyword(s):  
Graph Homology

scholarly journals KHOVANOV–ROZANSKY GRAPH HOMOLOGY AND COMPOSITION PRODUCT

2008 ◽  
Vol 17 (12) ◽  
pp. 1549-1559 ◽  
Author(s):  
E. WAGNER
Keyword(s):  
Recursive Formula ◽  
Graph Polynomial ◽  
Graph Homology ◽  
Composition Product

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.

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