A Boundary Operator for Simplices
Geometric Topology
2011-09-13 v1 Algebraic Topology
Abstract
We generalize the very well known boundary operator of the ordinary singular homology theory, defined in many books about algebraic topology. We describe a variant of this ordinary simplicial boundary operator where the usual boundary (n-1)-simplices of each n-simplex are replaced by combinations of internal (n-1)- simplices parallel to the faces. This construction may lead to an infinite class of extraordinary non-isomorphic homology theories. We show further some interesting constructions on the standard simplex.
Cite
@article{arxiv.1109.2161,
title = {A Boundary Operator for Simplices},
author = {Volker W. Thürey},
journal= {arXiv preprint arXiv:1109.2161},
year = {2011}
}
Comments
33 pages, 17 figures and diagrams