A notion of graph homeomorphism
General Topology
2014-01-14 v1 Discrete Mathematics
Abstract
We introduce a notion of graph homeomorphisms which uses the concept of dimension and homotopy for graphs. It preserves the dimension of a subbasis, cohomology and Euler characteristic. Connectivity and homotopy look as in classical topology. The Brouwer-Lefshetz fixed point leads to the following discretiszation of the Kakutani fixed point theorem: any graph homeomorphism T with nonzero Lefschetz number has a nontrivial invariant open set which is fixed by T.
Cite
@article{arxiv.1401.2819,
title = {A notion of graph homeomorphism},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:1401.2819},
year = {2014}
}
Comments
11 figures, 33 pages