Timeline for Cup products in the Mayer-Vietoris sequence

7 events

when toggle format	what		by	license	comment
Dec 26, 2018 at 4:10	comment	added	John Klein		"cones off" refers to the following: There is an inclusion $X = U \cup_{U\cap V} V \to CU \cup_{U\cap V} C V \simeq \Sigma (U\cap V)$, where $C$ means the unreduced cone.
Dec 26, 2018 at 4:05	comment	added	John Klein		I don't know of a reference; it's probably folklore. It is a reinterpretation that uses the Barratt-Puppe sequence. There's a cofiber sequence $X \to \Sigma (U \cap V) \to \Sigma U \vee \Sigma V$, where $\Sigma$ means unreduced suspension. The sequence wiill induce the Mayer-Vietoris sequence on cohomology.
Dec 25, 2018 at 20:06	comment	added	Chris Gerig		What is a reference for this description of the Mayer-Vietoris map $\delta^\ast$? I haven't seen it in Hatcher, Dold, Spanier, etc. (albeit the standard references seem to only elaborate on the homological MV unless it's using de Rham cohomology). I take it "cones off" means pinches off $U-(U\cap V)$ and $V-(U\cap V)$ separately in $X$. I like this description because then it's easy to see that elements in $Im(\delta^\ast)$ have trivial (cup product) square.
May 4, 2018 at 10:26	history	edited	John Klein	CC BY-SA 4.0	added 2 characters in body
May 3, 2018 at 23:12	vote	accept	FKranhold
May 3, 2018 at 20:39	history	edited	John Klein	CC BY-SA 4.0	added 4 characters in body
May 3, 2018 at 20:33	history	answered	John Klein	CC BY-SA 4.0