$q$-Analog Singular Homology of Convex Spaces

Details $q$-Analog Singular Homology of Convex Spaces $q$-Analog Singular Homology of Convex Spaces

2011-08-22

arxiv.org/abs/1108.4346v1

Mathematics

Algebraic Topology

16 pages. Some of these results were presented for the XVIII Congreso Colombiano de Matem\'aticas in Bucaramanga, 2011

Scientific paper

In this article we study some interesting properties of the $q$-Analog singular homology, which is a generalization of the usual singular homology, suitably adapted to the context of $N$-complex and amplitude homology \cite{kapranov}. We calculate the $q$-Analog singular homology of a convex space. Although it is a local matter; this is an important step in order to understand the presheaf of $q$-chains and its algebraic properties. Our result is consistent with those of Dubois-Viol\`ette & Henneaux \cite{dubois3}. Some of these results were presented for the XVIII Congreso Colombiano de Matem\'aticas in Bucaramanga, 2011.

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