Geodesic
Cuts and Flows of Cell Complexes
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

Voir la notice de l'article provenant de la source Episciences

We study the vector spaces and integer lattices of cuts and flows of an arbitrary finite CW complex, and their relationships to its critical group and related invariants. Our results extend the theory of cuts and flows in graphs, in particular the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and describe sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups; these are expressed as short exact sequences with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant. 
@article{DMTCS_2013_special_264_a65,
     author = {Duval, Art M. and Klivans, Caroline J. and Martin, Jeremy L.},
     title = {Cuts and {Flows} of {Cell} {Complexes}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.12794},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12794/}
}
TY  - JOUR
AU  - Duval, Art M.
AU  - Klivans, Caroline J.
AU  - Martin, Jeremy L.
TI  - Cuts and Flows of Cell Complexes
JO  - Discrete mathematics & theoretical computer science
PY  - 2013
VL  - DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12794/
DO  - 10.46298/dmtcs.12794
LA  - en
ID  - DMTCS_2013_special_264_a65
ER  - 
%0 Journal Article
%A Duval, Art M.
%A Klivans, Caroline J.
%A Martin, Jeremy L.
%T Cuts and Flows of Cell Complexes
%J Discrete mathematics & theoretical computer science
%D 2013
%V DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12794/
%R 10.46298/dmtcs.12794
%G en
%F DMTCS_2013_special_264_a65
Duval, Art M.; Klivans, Caroline J.; Martin, Jeremy L. Cuts and Flows of Cell Complexes. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.12794. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12794/

Cité par Sources :