Inducing a map on homology from a correspondence
Harker, Shaun
Kokubu, Hiroshi
Mischaikow, Konstantin
Pilarczyk, Pawel
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.
American Mathematical Society
2016
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doc-type:article
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https://research-explorer.app.ist.ac.at/record/1252
Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. <i>Proceedings of the American Mathematical Society</i>. 2016;144(4):1787-1801. doi:<a href="https://doi.org/10.1090/proc/12812">10.1090/proc/12812</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/12812
info:eu-repo/grantAgreement/EC/FP7/622033
info:eu-repo/semantics/closedAccess