Morse theory for complexes of groups
We construct an equivariant version of discrete Morse theory for simplicial complexes endowed with group actions. The key ingredient is a 2-categorical criterion for making acyclic partial matchings on the quotient space compatible with an overlaid complex of groups. We use the discrete flow categor...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2024
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| _version_ | 1811139736016781312 |
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| author | Yerolemou, N Nanda, V |
| author_facet | Yerolemou, N Nanda, V |
| author_sort | Yerolemou, N |
| collection | OXFORD |
| description | We construct an equivariant version of discrete Morse theory for simplicial complexes endowed with group actions. The key ingredient is a 2-categorical criterion for making acyclic partial matchings on the quotient space compatible with an overlaid complex of groups. We use the discrete flow category of any such compatible matching to build the corresponding Morse complex of groups. Our main result establishes that the development of the Morse complex of groups recovers the original simplicial complex up to equivariant homotopy equivalence. |
| first_indexed | 2024-03-07T08:15:55Z |
| format | Journal article |
| id | oxford-uuid:99b76276-463d-4cae-8c23-34a1658a5810 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:10:49Z |
| publishDate | 2024 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:99b76276-463d-4cae-8c23-34a1658a58102024-06-14T15:36:32ZMorse theory for complexes of groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:99b76276-463d-4cae-8c23-34a1658a5810EnglishSymplectic ElementsElsevier2024Yerolemou, NNanda, VWe construct an equivariant version of discrete Morse theory for simplicial complexes endowed with group actions. The key ingredient is a 2-categorical criterion for making acyclic partial matchings on the quotient space compatible with an overlaid complex of groups. We use the discrete flow category of any such compatible matching to build the corresponding Morse complex of groups. Our main result establishes that the development of the Morse complex of groups recovers the original simplicial complex up to equivariant homotopy equivalence. |
| spellingShingle | Yerolemou, N Nanda, V Morse theory for complexes of groups |
| title | Morse theory for complexes of groups |
| title_full | Morse theory for complexes of groups |
| title_fullStr | Morse theory for complexes of groups |
| title_full_unstemmed | Morse theory for complexes of groups |
| title_short | Morse theory for complexes of groups |
| title_sort | morse theory for complexes of groups |
| work_keys_str_mv | AT yerolemoun morsetheoryforcomplexesofgroups AT nandav morsetheoryforcomplexesofgroups |