Hopfian and co-Hopfian $G$-CW-complexes
HTML articles powered by AMS MathViewer
- by Goutam Mukherjee PDF
- Proc. Amer. Math. Soc. 125 (1997), 1229-1236 Request permission
Abstract:
We determine conditions for a $G$-CW-complex to be a Hopfian or a co-Hopfian object in the $G$-homotopy category of $G$-path-connected $G$-CW-complexes with base points.References
- Gilbert Baumslag, Hopficity and abelian groups, Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman & Co., Chicago, Ill., 1963, pp. 331–335. MR 0169896
- Glen E. Bredon, Equivariant cohomology theories, Lecture Notes in Mathematics, No. 34, Springer-Verlag, Berlin-New York, 1967. MR 0214062, DOI 10.1007/BFb0082690
- Tammo tom Dieck, Transformation groups, De Gruyter Studies in Mathematics, vol. 8, Walter de Gruyter & Co., Berlin, 1987. MR 889050, DOI 10.1515/9783110858372.312
- A. D. Elmendorf, Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983), no. 1, 275–284. MR 690052, DOI 10.1090/S0002-9947-1983-0690052-0
- Peter Hilton and Joseph Roitberg, Note on epimorphisms and monomorphisms in homotopy theory, Proc. Amer. Math. Soc. 90 (1984), no. 2, 316–320. MR 727257, DOI 10.1090/S0002-9939-1984-0727257-2
- Peter Hilton and Joseph Roitberg, Relative epimorphisms and monomorphisms in homotopy theory, Compositio Math. 61 (1987), no. 3, 353–367. MR 883488
- V. A. Hiremath, Hopfian rings and Hopfian modules, Indian J. Pure Appl. Math. 17 (1986), no. 7, 895–900. MR 851881
- Morris Orzech and Luis Ribes, Residual finiteness and the Hopf property in rings, J. Algebra 15 (1970), 81–88. MR 255587, DOI 10.1016/0021-8693(70)90087-6
- Joseph Roitberg, Monomorphisms and epimorphisms in homotopy theory, Israel J. Math. 46 (1983), no. 3, 205–211. MR 733350, DOI 10.1007/BF02761953
- Joseph Roitberg, Residually finite, Hopfian and co-Hopfian spaces, Conference on algebraic topology in honor of Peter Hilton (Saint John’s, Nfld., 1983) Contemp. Math., vol. 37, Amer. Math. Soc., Providence, RI, 1985, pp. 131–144. MR 789801, DOI 10.1090/conm/037/789801
- K. Varadarajan, Hopfian and co-Hopfian objects, Publ. Mat. 36 (1992), no. 1, 293–317. MR 1179618, DOI 10.5565/PUBLMAT_{3}6192_{2}1
Additional Information
- Goutam Mukherjee
- Affiliation: School of Mathematics, SPIC Science Foundation, 92, G. N. Chetty Road, Madras-17, India
- Address at time of publication: Stat-Math Unit, Indian Statistical Institute, 203, B.T. Road, Calcutta-35, India
- Email: goutam@ssf.ernet.in, goutam@isical.ernet.in
- Received by editor(s): August 21, 1995
- Communicated by: Thomas Goodwillie
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1229-1236
- MSC (1991): Primary 55N25, 55P10
- DOI: https://doi.org/10.1090/S0002-9939-97-03778-7
- MathSciNet review: 1372041