Balanced Fiber Bundles and GKM Theory
Let T be a torus and B a compact T-manifold. Goresky et al. show in [3] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H*[over]T(B) as a subring of H*[over]T(B[superscript 2]). In this paper, we prov...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Oxford University Press
2015
|
| Online Access: | http://hdl.handle.net/1721.1/92866 https://orcid.org/0000-0003-2641-1097 |
| _version_ | 1826188221185261568 |
|---|---|
| author | Guillemin, Victor W. Sabatini, Silvia Zara, Catalin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Guillemin, Victor W. Sabatini, Silvia Zara, Catalin |
| author_sort | Guillemin, Victor W. |
| collection | MIT |
| description | Let T be a torus and B a compact T-manifold. Goresky et al. show in [3] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H*[over]T(B) as a subring of H*[over]T(B[superscript 2]). In this paper, we prove an analog of this result for T-equivariant fiber bundles: we show that if M is a T-manifold and π:M→B a fiber bundle for which π intertwines the two T-actions, there is a simple combinatorial description of H*[over]T(M) as a subring of H*[over]T(π[superscript -1](B[superscript T])). Using this result, we obtain fiber bundle analogs of results of Guillemin et al. on GKM theory for homogeneous spaces. |
| first_indexed | 2024-09-23T07:56:05Z |
| format | Article |
| id | mit-1721.1/92866 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:56:05Z |
| publishDate | 2015 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | mit-1721.1/928662022-09-30T01:06:39Z Balanced Fiber Bundles and GKM Theory Guillemin, Victor W. Sabatini, Silvia Zara, Catalin Massachusetts Institute of Technology. Department of Mathematics Guillemin, Victor W. Let T be a torus and B a compact T-manifold. Goresky et al. show in [3] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H*[over]T(B) as a subring of H*[over]T(B[superscript 2]). In this paper, we prove an analog of this result for T-equivariant fiber bundles: we show that if M is a T-manifold and π:M→B a fiber bundle for which π intertwines the two T-actions, there is a simple combinatorial description of H*[over]T(M) as a subring of H*[over]T(π[superscript -1](B[superscript T])). Using this result, we obtain fiber bundle analogs of results of Guillemin et al. on GKM theory for homogeneous spaces. 2015-01-14T19:41:49Z 2015-01-14T19:41:49Z 2012-07 2012-05 Article http://purl.org/eprint/type/JournalArticle 1073-7928 1687-0247 http://hdl.handle.net/1721.1/92866 Guillemin, V., S. Sabatini, and C. Zara. “Balanced Fiber Bundles and GKM Theory.” International Mathematics Research Notices (July 9, 2012). vol. 2013 (17): 3886-3910. https://orcid.org/0000-0003-2641-1097 en_US http://dx.doi.org/10.1093/imrn/rns168 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press arXiv |
| spellingShingle | Guillemin, Victor W. Sabatini, Silvia Zara, Catalin Balanced Fiber Bundles and GKM Theory |
| title | Balanced Fiber Bundles and GKM Theory |
| title_full | Balanced Fiber Bundles and GKM Theory |
| title_fullStr | Balanced Fiber Bundles and GKM Theory |
| title_full_unstemmed | Balanced Fiber Bundles and GKM Theory |
| title_short | Balanced Fiber Bundles and GKM Theory |
| title_sort | balanced fiber bundles and gkm theory |
| url | http://hdl.handle.net/1721.1/92866 https://orcid.org/0000-0003-2641-1097 |
| work_keys_str_mv | AT guilleminvictorw balancedfiberbundlesandgkmtheory AT sabatinisilvia balancedfiberbundlesandgkmtheory AT zaracatalin balancedfiberbundlesandgkmtheory |