Timeline for Using Stiefel-Whitney class to build new principal bundles

11 events

when toggle format	what		by	license	comment
Jun 25, 2019 at 18:58	answer	added	user43326		timeline score: 4
Jun 25, 2019 at 13:10	history	edited	Leonardo Schultz	CC BY-SA 4.0	edited title
Jun 25, 2019 at 12:40	comment	added	David Roberts♦		The Lie algebras of $SU(2)$ and $SO(3)$ are canonically isomorphic, so local connection forms for both bundles are essentially valued in the same Lie algebra, and the conjugation action of the structure group that appears in the formula on overlaps is the same for the original transition functions and the lifted ones.
Jun 25, 2019 at 12:38	history	edited	Martin Sleziak	CC BY-SA 4.0	added the (stiefel-whitney) tag
Jun 25, 2019 at 12:29	comment	added	Ulrich Pennig		$SU(2)$ is a $2$-fold cover of $SO(3)$. In particular, there is a quotient map $q : SU(2) \to SO(3)$. $P$ is covered by a principal $SU(2)$-bundle $Q$ if the bundle projection $Q \to R^2 \times \Sigma$ factors through $P$ and $Q$ is an $SU(2)$-bundle in such a way that the $SU(2)$-multiplication is compatible with the $SO(3)$ multiplication on $P$.
Jun 25, 2019 at 12:23	history	edited	Leonardo Schultz	CC BY-SA 4.0	deleted 15 characters in body
Jun 25, 2019 at 12:09	comment	added	Oliver Nash		The keywords you're looking for are "spin structure": en.wikipedia.org/wiki/Spin_structure
Jun 25, 2019 at 11:09	history	edited	user43326		Added a tag.
Jun 25, 2019 at 10:56	history	edited	Leonardo Schultz	CC BY-SA 4.0	edited title
Jun 25, 2019 at 8:35	review	Close votes
Jun 28, 2019 at 16:21
Jun 25, 2019 at 7:52	history	asked	Leonardo Schultz	CC BY-SA 4.0