{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:42:21Z","timestamp":1760031741692,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T00:00:00Z","timestamp":1743465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12371068","DMS 1641020"],"award-info":[{"award-number":["12371068","DMS 1641020"]}]},{"name":"National Science Foundation","award":["12371068","DMS 1641020"],"award-info":[{"award-number":["12371068","DMS 1641020"]}]},{"name":"Huazhong University of Science and Technology","award":["12371068","DMS 1641020"],"award-info":[{"award-number":["12371068","DMS 1641020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/axioms14040267","type":"journal-article","created":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T11:17:57Z","timestamp":1743506277000},"page":"267","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quasi-Elliptic Cohomology of 4-Spheres"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-3564-4821","authenticated-orcid":false,"given":"Zhen","family":"Huan","sequence":"first","affiliation":[{"name":"Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s00220-023-04929-w","article-title":"Cyclification of Orbifolds","volume":"405","author":"Sati","year":"2024","journal-title":"Comm. 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