Note on epimorphisms and monomorphisms in homotopy theory
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- by Peter Hilton and Joseph Roitberg PDF
- Proc. Amer. Math. Soc. 90 (1984), 316-320 Request permission
Abstract:
We study epimorphisms $e:X \to X$ and monomorphisms $m:X \to X$ in the pointed homotopy category of path-connected CW-spaces. Our principal theorems allow us to infer that under suitable finiteness and fundamental group assumptions, such are in fact homotopy equivalences.References
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M. Castellet, P. Hilton and J. Roitberg, On pseudo-identities. II (in preparation).
- Peter Hilton, Guido Mislin, and Joe Roitberg, Localization of nilpotent groups and spaces, North-Holland Mathematics Studies, No. 15, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0478146
- Peter Hilton and Joseph Roitberg, On pseudo-identities. I, Arch. Math. (Basel) 41 (1983), no. 3, 204–214. MR 721051, DOI 10.1007/BF01194830 H. Hopf, Beiträge zur Klassifizierung der Flächenabbildungen, J. Reine Angew. Math. 165 (1931), 225-236.
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 316-320
- MSC: Primary 55P10; Secondary 55P30
- DOI: https://doi.org/10.1090/S0002-9939-1984-0727257-2
- MathSciNet review: 727257