A Boundary Operator for Simplices

Volker W. Thürey

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arXiv · 1109.2161

A Boundary Operator for Simplices

Volker W. Thürey

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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.

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Volker W. Thürey. 2011-09-09. A Boundary Operator for Simplices. https://arxiv.org/abs/1109.2161

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