Quasi-Elliptic Cohomology of 4-Spheres
It is a famous hypothesis that orbifold D-brane charges in string theory can be classified in twisted equivariant K-theory. Recently, it is believed that the hypothesis has a non-trivial lift to M-branes classified in twisted real equivariant 4-Cohomotopy. Quasi-elliptic cohomology, which is defined...
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MDPI AG
2025-04-01
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| author | Zhen Huan |
| author_facet | Zhen Huan |
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| description | It is a famous hypothesis that orbifold D-brane charges in string theory can be classified in twisted equivariant K-theory. Recently, it is believed that the hypothesis has a non-trivial lift to M-branes classified in twisted real equivariant 4-Cohomotopy. Quasi-elliptic cohomology, which is defined as an equivariant cohomology of a cyclification of orbifolds, potentially interpolates the two statements, by approximating equivariant 4-Cohomotopy classified by 4-sphere orbifolds. In this paper we compute Real and complex quasi-elliptic cohomology theories of 4-spheres under the action by some finite subgroups that are the most interesting isotropy groups where the M5-branes may sit. The computation connects the M-brane charges in the presence of discrete symmetries to Real quasi-elliptic cohomology theories, and those with the symmetry omitted to complex quasi-elliptic cohomology theories. |
| format | Article |
| id | doaj-art-4cdbdf9f0a1440bf9f4ba5bd2a7821ee |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-4cdbdf9f0a1440bf9f4ba5bd2a7821ee2025-08-20T02:17:14ZengMDPI AGAxioms2075-16802025-04-0114426710.3390/axioms14040267Quasi-Elliptic Cohomology of 4-SpheresZhen Huan0Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, ChinaIt is a famous hypothesis that orbifold D-brane charges in string theory can be classified in twisted equivariant K-theory. Recently, it is believed that the hypothesis has a non-trivial lift to M-branes classified in twisted real equivariant 4-Cohomotopy. Quasi-elliptic cohomology, which is defined as an equivariant cohomology of a cyclification of orbifolds, potentially interpolates the two statements, by approximating equivariant 4-Cohomotopy classified by 4-sphere orbifolds. In this paper we compute Real and complex quasi-elliptic cohomology theories of 4-spheres under the action by some finite subgroups that are the most interesting isotropy groups where the M5-branes may sit. The computation connects the M-brane charges in the presence of discrete symmetries to Real quasi-elliptic cohomology theories, and those with the symmetry omitted to complex quasi-elliptic cohomology theories.https://www.mdpi.com/2075-1680/14/4/267elliptic cohomologyM5-branesKR-theory |
| spellingShingle | Zhen Huan Quasi-Elliptic Cohomology of 4-Spheres Axioms elliptic cohomology M5-branes KR-theory |
| title | Quasi-Elliptic Cohomology of 4-Spheres |
| title_full | Quasi-Elliptic Cohomology of 4-Spheres |
| title_fullStr | Quasi-Elliptic Cohomology of 4-Spheres |
| title_full_unstemmed | Quasi-Elliptic Cohomology of 4-Spheres |
| title_short | Quasi-Elliptic Cohomology of 4-Spheres |
| title_sort | quasi elliptic cohomology of 4 spheres |
| topic | elliptic cohomology M5-branes KR-theory |
| url | https://www.mdpi.com/2075-1680/14/4/267 |
| work_keys_str_mv | AT zhenhuan quasiellipticcohomologyof4spheres |