Filtered matchings and simplicial complexes
To any finite simplicial complex X, we associate a natural filtration starting from Chari and Joswig’s discrete Morse complex and abutting to the matching complex of X. This construction leads to the definition of several homology theories, which we compute in a number of examples. We also completel...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Combinatorial Mathematics Society of Australasia
2022
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| _version_ | 1797064492569329664 |
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| author | Celoria, D Yerolemou, N |
| author_facet | Celoria, D Yerolemou, N |
| author_sort | Celoria, D |
| collection | OXFORD |
| description | To any finite simplicial complex X, we associate a natural filtration starting from Chari and Joswig’s discrete Morse complex and abutting to the matching complex of X. This construction leads to the definition of several homology theories, which we compute in a number of examples. We also completely determine the graded object associated to this filtration in terms of the homology of simpler complexes. This last result provides some connections to the number of vertex-disjoint cycles of a graph. |
| first_indexed | 2024-03-06T21:15:06Z |
| format | Journal article |
| id | oxford-uuid:3f84f174-53d4-4300-89a1-4671ef4f2003 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:15:06Z |
| publishDate | 2022 |
| publisher | Combinatorial Mathematics Society of Australasia |
| record_format | dspace |
| spelling | oxford-uuid:3f84f174-53d4-4300-89a1-4671ef4f20032022-03-26T14:32:40ZFiltered matchings and simplicial complexesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3f84f174-53d4-4300-89a1-4671ef4f2003EnglishSymplectic ElementsCombinatorial Mathematics Society of Australasia2022Celoria, DYerolemou, NTo any finite simplicial complex X, we associate a natural filtration starting from Chari and Joswig’s discrete Morse complex and abutting to the matching complex of X. This construction leads to the definition of several homology theories, which we compute in a number of examples. We also completely determine the graded object associated to this filtration in terms of the homology of simpler complexes. This last result provides some connections to the number of vertex-disjoint cycles of a graph. |
| spellingShingle | Celoria, D Yerolemou, N Filtered matchings and simplicial complexes |
| title | Filtered matchings and simplicial complexes |
| title_full | Filtered matchings and simplicial complexes |
| title_fullStr | Filtered matchings and simplicial complexes |
| title_full_unstemmed | Filtered matchings and simplicial complexes |
| title_short | Filtered matchings and simplicial complexes |
| title_sort | filtered matchings and simplicial complexes |
| work_keys_str_mv | AT celoriad filteredmatchingsandsimplicialcomplexes AT yerolemoun filteredmatchingsandsimplicialcomplexes |