Timeline for Vector bundles, finitely generated projective module?

7 events

when toggle format	what		by	license	comment
Jun 22, 2022 at 8:13	history	edited	CommunityBot		replaced http://math.uga.edu/~pete with http://alpha.math.uga.edu/~pete
Jan 29, 2016 at 18:57	history	edited	Pete L. Clark	CC BY-SA 3.0	added 10 characters in body
Dec 23, 2015 at 1:26	history	edited	Pete L. Clark	CC BY-SA 3.0	added 1586 characters in body
Dec 22, 2015 at 20:11	comment	added	Pete L. Clark		Agree with @Qiaochu.
Dec 22, 2015 at 19:06	comment	added	Qiaochu Yuan		@Nicola: it's not. Everything we're discussing only applies to vector bundles which are direct summands of trivial vector bundles. These are controlled in a formal categorical way by $\mathbb{R}(B)$.
Dec 22, 2015 at 17:56	comment	added	Nicola Ciccoli		In the original Swan paper (which is free access ams.org/journals/tran/1962-105-02/S0002-9947-1962-0143225-6/… ) normality of the base space is used to prove that two vector bundles are isomorphic iff their modules of sections are. I failed to understand where this specific condition can be relaxed in Tychonoff (i.e. Hausdorff and completely regular). A question of some interest because I remember reading that Tychonoff is the minimal topological condition under which it is possibile to fully recover $B$ from $\mathbb R(B)$.
Dec 22, 2015 at 11:03	history	answered	Pete L. Clark	CC BY-SA 3.0