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Graph Approach to the Computation of the Homology of Continuous Maps

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Abstract

We introduce an efficient algorithm to compute the homomorphism induced in (relative) homology by a continous map. The algorithm is based on a cubical approximation of the map and the theory of multivalued maps. A software implementation of the algorithms introduced in this paper is available at [27].

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Authors and Affiliations

  1. 1School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA

    Konstantin Mischaikow

  2. Division of Computational Mathematics, Graduate School of Business, ul. Zielona 27 33-300 Nowy Sacz, Poland and Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30-072 Krakow, Poland

    Marian Mrozek

  3. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA and Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow, Poland

    Pawel Pilarczyk

Authors
  1. Konstantin Mischaikow
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  2. Marian Mrozek
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  3. Pawel Pilarczyk
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Correspondence to Konstantin Mischaikow, Marian Mrozek or Pawel Pilarczyk.

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Mischaikow, K., Mrozek, M. & Pilarczyk, P. Graph Approach to the Computation of the Homology of Continuous Maps. Found Comput Math 5, 199–229 (2005). https://doi.org/10.1007/s10208-004-0125-2

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  • DOI: https://doi.org/10.1007/s10208-004-0125-2

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