Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants
In this paper, we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space Σ with singular stratum (a closed manifold of positive codimension) and associated link equal to , a smooth compact manifold. We briefly call such spaces manifolds with -fibered...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2021 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211361 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants. Boris Botvinnik, Paolo Piazza and Jonathan Rosenberg. SIGMA 17 (2021), 062, 39 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713928079900672 |
|---|---|
| author | Botvinnik, Boris Piazza, Paolo Rosenberg, Jonathan |
| author_facet | Botvinnik, Boris Piazza, Paolo Rosenberg, Jonathan |
| citation_txt | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants. Boris Botvinnik, Paolo Piazza and Jonathan Rosenberg. SIGMA 17 (2021), 062, 39 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space Σ with singular stratum (a closed manifold of positive codimension) and associated link equal to , a smooth compact manifold. We briefly call such spaces manifolds with -fibered singularities. Under suitable spin assumptions, we give necessary index-theoretic conditions for the existence of wedge metrics of positive scalar curvature. Assuming in addition that is a simply connected homogeneous space of positive scalar curvature, = /, with the semisimple compact Lie group acting transitively on by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed enough for large classes of examples, even when Σ and are not simply connected. We also investigate the space of such psc metrics and show that it often splits into many cobordism classes.
|
| first_indexed | 2026-03-20T00:04:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211361 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T00:04:06Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Botvinnik, Boris Piazza, Paolo Rosenberg, Jonathan 2025-12-30T15:55:58Z 2021 Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants. Boris Botvinnik, Paolo Piazza and Jonathan Rosenberg. SIGMA 17 (2021), 062, 39 pages 1815-0659 2020 Mathematics Subject Classification: 53C21; 58J22; 53C27; 19L41; 55N22; 58J28 arXiv:2005.02744 https://nasplib.isofts.kiev.ua/handle/123456789/211361 https://doi.org/10.3842/SIGMA.2021.062 In this paper, we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space Σ with singular stratum (a closed manifold of positive codimension) and associated link equal to , a smooth compact manifold. We briefly call such spaces manifolds with -fibered singularities. Under suitable spin assumptions, we give necessary index-theoretic conditions for the existence of wedge metrics of positive scalar curvature. Assuming in addition that is a simply connected homogeneous space of positive scalar curvature, = /, with the semisimple compact Lie group acting transitively on by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed enough for large classes of examples, even when Σ and are not simply connected. We also investigate the space of such psc metrics and show that it often splits into many cobordism classes. We thank the Mathematisches Forschungsinstitut Oberwolfach for hosting Workshop 1732 in 2017 on Analysis, Geometry and Topology of Positive Scalar Curvature Metrics, which marked the start of this project. This work was also supported by U.S. NSF grant number DMS-1607162, by Simons Foundation Collaboration Grant number 708183, by Sapienza Universita di Roma, and by the Ministero Istruzione Universita e Ricerca through the PRIN Spazi di Moduli e Teoria di Lie. B.B. and J.R. acknowledge a very pleasant and productive visit to Rome in MayJune 2019, as well as a visit by J.R. to Rome in January 2020. P.P. thanks Pierre Albin and Jesse Gell-Redman for interesting discussions about the content of Section 2. We would like to thank the referees of this article for a careful reading of the previous drafts and for their suggestions for improvements. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants Article published earlier |
| spellingShingle | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants Botvinnik, Boris Piazza, Paolo Rosenberg, Jonathan |
| title | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants |
| title_full | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants |
| title_fullStr | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants |
| title_full_unstemmed | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants |
| title_short | Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants |
| title_sort | positive scalar curvature on spin pseudomanifolds: the fundamental group and secondary invariants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211361 |
| work_keys_str_mv | AT botvinnikboris positivescalarcurvatureonspinpseudomanifoldsthefundamentalgroupandsecondaryinvariants AT piazzapaolo positivescalarcurvatureonspinpseudomanifoldsthefundamentalgroupandsecondaryinvariants AT rosenbergjonathan positivescalarcurvatureonspinpseudomanifoldsthefundamentalgroupandsecondaryinvariants |