Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities
In this paper, we study manifolds, Σ, with fibred singularities, more specifically, a relevant space ᵖˢᶜ(Σ) of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space ᵖˢᶜ(Σ) is homotopy invariant under certain surgeries on Σ.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2021 |
| ISSN: | 1815-0659 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211315 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities. Boris Botvinnik and Mark G. Walsh. SIGMA 17 (2021), 034, 27 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862711328506904576 |
|---|---|
| author | Botvinnik, Boris Walsh, Mark G. |
| author_facet | Botvinnik, Boris Walsh, Mark G. |
| citation_txt | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities. Boris Botvinnik and Mark G. Walsh. SIGMA 17 (2021), 034, 27 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we study manifolds, Σ, with fibred singularities, more specifically, a relevant space ᵖˢᶜ(Σ) of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space ᵖˢᶜ(Σ) is homotopy invariant under certain surgeries on Σ.
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| first_indexed | 2026-03-19T15:15:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211315 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T15:15:19Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Botvinnik, Boris Walsh, Mark G. 2025-12-29T11:09:33Z 2021 Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities. Boris Botvinnik and Mark G. Walsh. SIGMA 17 (2021), 034, 27 pages 1815-0659 2020 Mathematics Subject Classification: 53C27; 57R65; 58J05; 58J50 arXiv:2005.03073 https://nasplib.isofts.kiev.ua/handle/123456789/211315 https://doi.org/10.3842/SIGMA.2021.034 In this paper, we study manifolds, Σ, with fibred singularities, more specifically, a relevant space ᵖˢᶜ(Σ) of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space ᵖˢᶜ(Σ) is homotopy invariant under certain surgeries on Σ. BB was partially supported by Simons Collaboration Grant 708183. We thank the referees for their careful reading and thoughtful comments. The second author would like to thank David Wraith for some productive conversations. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities Article published earlier |
| spellingShingle | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities Botvinnik, Boris Walsh, Mark G. |
| title | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities |
| title_full | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities |
| title_fullStr | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities |
| title_full_unstemmed | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities |
| title_short | Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities |
| title_sort | homotopy invariance of the space of metrics with positive scalar curvature on manifolds with singularities |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211315 |
| work_keys_str_mv | AT botvinnikboris homotopyinvarianceofthespaceofmetricswithpositivescalarcurvatureonmanifoldswithsingularities AT walshmarkg homotopyinvarianceofthespaceofmetricswithpositivescalarcurvatureonmanifoldswithsingularities |