On flat manifold bundles and the connectivity of Haefliger’s classifying spaces
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- by Sam Nariman;
- Proc. Amer. Math. Soc. 152 (2024), 4943-4957
- DOI: https://doi.org/10.1090/proc/16941
- Published electronically: September 24, 2024
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Abstract:
We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston’s conjecture predicts that every $M$-bundle over a manifold $B$ where $\operatorname {dim}(B)\leq \operatorname {dim}(M)$ is cobordant to a flat $M$-bundle. In particular, we study the bordism class of flat $M$-bundles over low dimensional manifolds, comparing a finite dimensional Lie group $G$ with $\mathrm {Diff}_0(G)$.References
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Bibliographic Information
- Sam Nariman
- Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
- MR Author ID: 1228088
- ORCID: 0000-0002-9193-9587
- Email: snariman@purdue.edu
- Received by editor(s): August 26, 2022
- Received by editor(s) in revised form: March 9, 2024, March 11, 2024, and May 14, 2024
- Published electronically: September 24, 2024
- Additional Notes: The author was partially supported by NSF CAREER Grant DMS-2239106, NSF DMS-2113828 and Simons Foundation (855209, SN)
- Communicated by: Julie Bergner
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 4943-4957
- MSC (2020): Primary 57R30, 57R32, 57S05, 58H10, 55R40; Secondary 58D05
- DOI: https://doi.org/10.1090/proc/16941
- MathSciNet review: 4802645