Covering Groups of Nonconnected Topological Groups and 2-Groups
| Autor: | Demyan Vakhrameev, Matthew Westaway, Dmitriy Rumynin |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Covering space Group Theory (math.GR) 010103 numerical & computational mathematics Primary 22E20 Secondary 18D05 20J05 01 natural sciences Mathematics::Algebraic Topology Mathematics::K-Theory and Homology Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Category Theory (math.CT) Topological group 0101 mathematics QA Category theory 2-group Mathematics Algebra and Number Theory Group extension 010102 general mathematics Quantum algebra Mathematics - Category Theory Cohomology Mathematics - Group Theory Group theory |
| Zdroj: | Communications in Algebra |
| ISSN: | 0092-7872 |
| Popis: | We investigate the universal cover of a topological group that is not necessarily connected. Its existence as a topological group is governed by a Taylor cocycle, an obstruction in 3-cohomology. Alternatively, it always exists as a topological 2-group. The splitness of this 2-group is also governed by an obstruction in 3-cohomology, a Sinh cocycle. We give explicit formulas for both obstructions and show that they are inverse of each other. 9 pages. Version 2: historical review added. Version 3 (14 pages): historical review revised, minor corrections elsewhere, some of the results did not make it into the final version. Version 4: final journal version with a slightly different (to Version 3) approach |
| Databáze: | OpenAIRE |
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