Graph approach to the computation of the homology of continuous maps

Konstantin Mischaikow; Marian Mrozek; Pawel Pilarczyk

doi:10.1007/s10208-004-0125-2

Graph approach to the computation of the homology of continuous maps

Konstantin Mischaikow, Marian Mrozek, Pawel Pilarczyk

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

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].

Original language	English (US)
Pages (from-to)	199-229
Number of pages	31
Journal	Foundations of Computational Mathematics
Volume	5
Issue number	2
DOIs	https://doi.org/10.1007/s10208-004-0125-2
State	Published - Apr 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Keywords

Computational homology
Cubical complexes
Homology maps

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10.1007/s10208-004-0125-2

Cite this

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title = "Graph approach to the computation of the homology of continuous maps",

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].",

keywords = "Computational homology, Cubical complexes, Homology maps",

author = "Konstantin Mischaikow and Marian Mrozek and Pawel Pilarczyk",

year = "2005",

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doi = "10.1007/s10208-004-0125-2",

language = "English (US)",

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T1 - Graph approach to the computation of the homology of continuous maps

AU - Mischaikow, Konstantin

AU - Mrozek, Marian

AU - Pilarczyk, Pawel

PY - 2005/4

Y1 - 2005/4

N2 - 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].

AB - 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].

KW - Computational homology

KW - Cubical complexes

KW - Homology maps

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JO - Foundations of Computational Mathematics

JF - Foundations of Computational Mathematics

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ER -

Graph approach to the computation of the homology of continuous maps

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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