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Hopfian and co-Hopfian -CW-complexes
Author:
Goutam Mukherjee
Journal:
Proc. Amer. Math. Soc. 125 (1997), 1229-1236
MSC (1991):
Primary 55N25, 55P10
MathSciNet review:
1372041
Full-text PDF Free Access
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Additional Information
Abstract: We determine conditions for a -CW-complex to be a Hopfian or a co-Hopfian object in the -homotopy category of -path-connected -CW-complexes with base points.
- 1.
Gilbert
Baumslag, Hopficity and abelian groups, Topics in Abelian
Groups (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman and
Co., Chicago, Ill., 1963, pp. 331–335. MR 0169896
(30 #139)
- 2.
Glen
E. Bredon, Equivariant cohomology theories, Lecture Notes in
Mathematics, No. 34, Springer-Verlag, Berlin, 1967. MR 0214062
(35 #4914)
- 3.
Tammo
tom Dieck, Transformation groups, de Gruyter Studies in
Mathematics, vol. 8, Walter de Gruyter & Co., Berlin, 1987. MR 889050
(89c:57048)
- 4.
A.
D. Elmendorf, Systems of fixed point sets,
Trans. Amer. Math. Soc. 277 (1983),
no. 1, 275–284. MR 690052
(84f:57029), http://dx.doi.org/10.1090/S0002-9947-1983-0690052-0
- 5.
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 (85j:55014), http://dx.doi.org/10.1090/S0002-9939-1984-0727257-2
- 6.
Peter
Hilton and Joseph
Roitberg, Relative epimorphisms and monomorphisms in homotopy
theory, Compositio Math. 61 (1987), no. 3,
353–367. MR
883488 (88d:55012)
- 7.
V.
A. Hiremath, Hopfian rings and Hopfian modules, Indian J. Pure
Appl. Math. 17 (1986), no. 7, 895–900. MR 851881
(87i:16031)
- 8.
Morris
Orzech and Luis
Ribes, Residual finiteness and the Hopf property in rings, J.
Algebra 15 (1970), 81–88. MR 0255587
(41 #248)
- 9.
Joseph
Roitberg, Monomorphisms and epimorphisms in homotopy theory,
Israel J. Math. 46 (1983), no. 3, 205–211. MR 733350
(85i:55010), http://dx.doi.org/10.1007/BF02761953
- 10.
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
(86i:55009), http://dx.doi.org/10.1090/conm/037/789801
- 11.
K.
Varadarajan, Hopfian and co-Hopfian objects, Publ. Mat.
36 (1992), no. 1, 293–317. MR 1179618
(93i:16002), http://dx.doi.org/10.5565/PUBLMAT_36192_21
- 1.
- G. Baumslag, Hopficity and Abelian groups, Topics in Abelian groups, Proc. Symp. on Abelian groups, New Mexico State Univ., 1962, 331-335. MR 30:139
- 2.
- G. E. Bredon, Equivariant Cohomology Theories, Lec. Notes in Math., Springer-Verlag, 1967. MR 35:4914
- 3.
- T. tom Dieck, Transformation groups, Walter de Gruyter, 1987. MR 89c:57048
- 4.
- A. D. Elmendorf, System of fixed point sets, Trans. Amer. Math. Soc., 227,1983, 275-284. MR 84f:57029
- 5.
- P. Hilton and J. Roitberg, Note on epimorphisms and monomorphisms in homotopy theory, Proc. Amer. Math. Soc., 90, 1984, 316-320. MR 85j:55014
- 6.
- P. Hilton and J. Roitberg, Relative epimorphisms and monomorphisms in homotopy theory, Compositio Math., 61, 1987, 353-367. MR 88d:55012
- 7.
- V. A. Hiremath, Hopfian rings and Hopfian modules, Indian J. Pure and Appl. Math., 17, 1986, 895-900. MR 87i:16031
- 8.
- M. Orzech and L. Ribes, Residual finiteness and the Hopf property of rings, J. Alg., 15, 1970, 81-88. MR 41:248
- 9.
- J. Roitberg, Monomorphisms and epimorphisms in homotopy theory, Israel J. Math., 46, 1983, 205-211. MR 85i:55010
- 10.
- J. Roitberg, Residually finite Hopfian and co-Hopfian spaces, Contemp. Math., 37, 1985, 131-144. MR 86i:55009
- 11.
- K. Varadarajan, Hopfian and co-Hopfian objects, Publicacions Matemàtiques, 36, 1992, 293-317. MR 93i:16002
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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
DOI:
http://dx.doi.org/10.1090/S0002-9939-97-03778-7
PII:
S 0002-9939(97)03778-7
Received by editor(s):
August 21, 1995
Communicated by:
Thomas Goodwillie
Article copyright:
© Copyright 1997 American Mathematical Society
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