A Boundary Operator for Simplices

Details A Boundary Operator for Simplices A Boundary Operator for Simplices

2011-09-09

arxiv.org/abs/1109.2161v1

Mathematics

Geometric Topology

33 pages, 17 figures and diagrams

Scientific paper

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.

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