paper
K-theory and limit-of-discrete-series for the universal cover of SL₂(R)
Jacek Brodzki · Graham Niblo · Roger Plymen · Nick Wright
Use in this reference: Linked institutional-repository preprint. Only introductory structural facts are summarized.
Relevant material: Section 1, page 2, describes the universal covering group and its center.
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| Universal cover of SL(2, R) | Definition | Section 1, page 2: the universal covering group of SL(2,R) |
| Universal cover of SL(2, R) | Center | Section 1, page 2: infinite cyclic center and absence of nontrivial compact subgroups |
| Universal cover of SL(2, R) | Global form | Section 1, page 2: structure of the universal cover |
| Universal cover of SL(2, R) | Maximal compact subgroup | Section 1, page 2: infinite cyclic center and absence of nontrivial compact subgroups |
| Universal cover of SL(2, R) | Global structure and topology | Section 1, page 2: structure of the universal cover |
| Universal cover of SL(2, R) | Explicit homomorphism | Section 1, page 2: structure of the universal cover |
| Universal SL(2,R) cover → SL(2,R) | Definition | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Domain | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Codomain | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Specified homomorphism | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Kernel | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Image | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Injective | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Surjective | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Covering degree | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Global and representation consequences | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Domain group | Section 1, page 2: universal cover and its infinite cyclic center |
| Universal SL(2,R) cover → SL(2,R) | Codomain group | Section 1, page 2: universal cover and its infinite cyclic center |