Discrete Morse theoretic algorithms for computing homology of complexes and maps
We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) c...
| Main Authors: | , , , |
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| Format: | Journal article |
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Springer Verlag
2013
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| _version_ | 1797093983396036608 |
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| author | Harker, S Mischaikow, K Mrozek, M Nanda, V |
| author_facet | Harker, S Mischaikow, K Mrozek, M Nanda, V |
| author_sort | Harker, S |
| collection | OXFORD |
| description | We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that function is subject to measurement errors. We introduce a new Morse theoretic preprocessing framework for deriving chain maps from such set-valued maps, and hence provide an effective scheme for computing the morphism induced on homology by the approximated continuous function. |
| first_indexed | 2024-03-07T04:07:52Z |
| format | Journal article |
| id | oxford-uuid:c6d4c567-f9fe-424c-a30f-26e635a1bc1b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:07:52Z |
| publishDate | 2013 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:c6d4c567-f9fe-424c-a30f-26e635a1bc1b2022-03-27T06:40:40ZDiscrete Morse theoretic algorithms for computing homology of complexes and mapsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c6d4c567-f9fe-424c-a30f-26e635a1bc1bSymplectic Elements at OxfordSpringer Verlag2013Harker, SMischaikow, KMrozek, MNanda, VWe provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that function is subject to measurement errors. We introduce a new Morse theoretic preprocessing framework for deriving chain maps from such set-valued maps, and hence provide an effective scheme for computing the morphism induced on homology by the approximated continuous function. |
| spellingShingle | Harker, S Mischaikow, K Mrozek, M Nanda, V Discrete Morse theoretic algorithms for computing homology of complexes and maps |
| title | Discrete Morse theoretic algorithms for computing homology of complexes and maps |
| title_full | Discrete Morse theoretic algorithms for computing homology of complexes and maps |
| title_fullStr | Discrete Morse theoretic algorithms for computing homology of complexes and maps |
| title_full_unstemmed | Discrete Morse theoretic algorithms for computing homology of complexes and maps |
| title_short | Discrete Morse theoretic algorithms for computing homology of complexes and maps |
| title_sort | discrete morse theoretic algorithms for computing homology of complexes and maps |
| work_keys_str_mv | AT harkers discretemorsetheoreticalgorithmsforcomputinghomologyofcomplexesandmaps AT mischaikowk discretemorsetheoreticalgorithmsforcomputinghomologyofcomplexesandmaps AT mrozekm discretemorsetheoreticalgorithmsforcomputinghomologyofcomplexesandmaps AT nandav discretemorsetheoreticalgorithmsforcomputinghomologyofcomplexesandmaps |