Talk:Moore space (algebraic topology)

simply connected

according to hatcher, the Moore space should be simply connected, if n \ge 2--131.114.73.45 (talk) 08:10, 18 April 2013 (UTC)[reply]

Well, isn't that built into the definition? If only one H_n isn't zero, and n \ge 2 then H_1 is zero and its simply connected. Right? 67.198.37.16 (talk) 04:32, 6 May 2016 (UTC)[reply]

The fundamental group may still be perfect.--Cgqyyflz^? 18:12, 10 March 2017 (UTC)[reply]

Oh, ah, yes. Hmm. I'm adding a "citation needed" blip to the statement. 67.198.37.16 (talk) 19:29, 17 November 2023 (UTC)[reply]

I quote Hatcher, example 2.40 page 143 of the last edition available on his website on 9 March 2024: "It is probably best for the definition of a Moore space to include the condition that M(G,n) be simply connected if n>1. The spaces we construct will have this property". Hatcher does not say that the fact that only one homology group is non-vanishing implies simple connectedness. He put simple connectedness as part of his definition. 西米露喜欢橙子 (talk) 03:19, 9 March 2024 (UTC)[reply]