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Foundations of Computational Mathematics

, Volume 5, Issue 2, pp 199–229 | Cite as

Graph Approach to the Computation of the Homology of Continuous Maps

Article

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].

Computational homology Homology maps Cubical complexes 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.1School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332USA
  2. 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 KrakowPoland
  3. 3.School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA and Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072 KrakowPoland

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