proposition 14.33 $\SU(2)$ is the three-sphere
open in the book ·
parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1226
· p. 555
Rests on
- depends_on definition 14.32 The special unitary group in two dimensions ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-11 ¶
Supports
-
depends_on
corollary 14.38
$\SU(2)$ is the universal cover
¶
-
depends_on
proposition 14.31
$\SO(3,\R)$ is not simply connected
¶
- depends_on remark 29.12 The coordinate singularity, and what it is not ¶
- depends_on proposition 14.45 Which representations descend to $\SO(3,\R)$ ¶
-
depends_on
proposition 14.31
$\SO(3,\R)$ is not simply connected
¶
- depends_on lemma A.369 $\Phi$ is a two-sheeted covering ¶
-
depends_on
theorem 14.37
$\SU(2)$ is a two-to-one cover of $\SO(3,\R)$
¶
- depends_on corollary 14.38 $\SU(2)$ is the universal cover ¶ ↺
- depends_on lemma A.369 $\Phi$ is a two-sheeted covering ¶ ↺
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | The special unitary group in two dimensions | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1236 |
depends_on |
← | $\SU(2)$ is the universal cover | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1540 |
depends_on |
← | $\Phi$ is a two-sheeted covering | declared | appendices/A-long-proofs.tex:17757 |
depends_on |
← | $\SU(2)$ is a two-to-one cover of $\SO(3,\R)$ | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1451 |
proves |
← | ch:12-lie-groups-fibre-bundles@proof-11 | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1239 |