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Inducing a map on homology from a correspondence. (English) Zbl 1337.55006

Summary: We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points.

MSC:

55M99 Classical topics in algebraic topology
55-04 Software, source code, etc. for problems pertaining to algebraic topology

Software:

CAPD; CHomP; ChainCon
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Full Text: DOI arXiv

References:

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