Mapping class groups of h-cobordant manifolds
We prove that the mapping class group is not an h-cobordism invariant of high-dimensional manifolds by exhibiting h-cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli space of ‘h-block’ bundles and understand its difference with the...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S205050942510087X/type/journal_article |
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| _version_ | 1849236280774230016 |
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| author | Samuel Muñoz-Echániz |
| author_facet | Samuel Muñoz-Echániz |
| author_sort | Samuel Muñoz-Echániz |
| collection | DOAJ |
| description | We prove that the mapping class group is not an h-cobordism invariant of high-dimensional manifolds by exhibiting h-cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli space of ‘h-block’ bundles and understand its difference with the moduli space of ordinary block bundles. |
| format | Article |
| id | doaj-art-15b11b5d39954c7b8d12422ca0598d45 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-15b11b5d39954c7b8d12422ca0598d452025-08-20T04:02:22ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.10087Mapping class groups of h-cobordant manifoldsSamuel Muñoz-Echániz0https://orcid.org/0009-0006-4190-6417https://ror.org/013meh722 University of Cambridge , Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, United KingdomWe prove that the mapping class group is not an h-cobordism invariant of high-dimensional manifolds by exhibiting h-cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli space of ‘h-block’ bundles and understand its difference with the moduli space of ordinary block bundles.https://www.cambridge.org/core/product/identifier/S205050942510087X/type/journal_article57R8055R6057S0557N3757Q10 |
| spellingShingle | Samuel Muñoz-Echániz Mapping class groups of h-cobordant manifolds Forum of Mathematics, Sigma 57R80 55R60 57S05 57N37 57Q10 |
| title | Mapping class groups of h-cobordant manifolds |
| title_full | Mapping class groups of h-cobordant manifolds |
| title_fullStr | Mapping class groups of h-cobordant manifolds |
| title_full_unstemmed | Mapping class groups of h-cobordant manifolds |
| title_short | Mapping class groups of h-cobordant manifolds |
| title_sort | mapping class groups of h cobordant manifolds |
| topic | 57R80 55R60 57S05 57N37 57Q10 |
| url | https://www.cambridge.org/core/product/identifier/S205050942510087X/type/journal_article |
| work_keys_str_mv | AT samuelmunozechaniz mappingclassgroupsofhcobordantmanifolds |