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The Mislin genus, phantom maps and weak identities

✍ Scribed by Ilyong Do; Jianzhong Pan


Book ID
104295558
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
55 KB
Volume
102
Category
Article
ISSN
0166-8641

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✦ Synopsis


For a nilpotent space X, we prove that the cardinality of the set WI(X), which denotes the homotopy classes of weak identities, depends only on the Mislin genus of X. On the other hand, we prove that when X = BG, the classifying space of a connected finite loop space, or X is a 1connected finite Postnikov space, or X is a 1-connected infinite loop space, and Y is the iterated loop space of a 1-connected finite CW-complex, the isomorphism class of the group Ph(X, Y ) depends only on the Mislin genus of X. These generalize recent results of Roitberg.


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