Topological bordism of singular spaces and an application to stratified L-classes
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly, instead of restricting geometric cycles by conditions on lin...
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1 January 2024
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| In: |
Topology and its applications
Year: 2024, Volume: 341, Pages: 1-26 |
| DOI: | 10.1016/j.topol.2023.108744 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.topol.2023.108744 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0166864123003371 
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| Author Notes: | Martin Rabel |
| Summary: | A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly, instead of restricting geometric cycles by conditions on links only, a more flexible framework is built directly via geometric properties, secondly, controlled topology methods are used to give an accessible link-based criterion to detect suitable cycles and thirdly, a geometric argument is used to show, that these classes of cycles are suitable to study the transition to intrinsic stratifications. As an application, we give a construction of topologically (homeomorphism) invariant (homological) L-classes on MHSS Witt-spaces satisfying conditions on Whitehead-groups of links and the dimensional spacing of meeting strata. These L-classes agree, whenever those spaces are additionally pl-pseudomanifolds, with the Goresky-MacPherson L-classes. |
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| Item Description: | Online verfügbar 5 October 2023, Version des Artikels 10 October 2023 Gesehen am 03.05.2024 This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.topol.2023.108744 |