Compact $3$-manifolds with infinitely-generated groups of self-homotopy-equivalences
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- by Darryl McCullough PDF
- Proc. Amer. Math. Soc. 91 (1984), 625-629 Request permission
Abstract:
Examples are constructed of compact $3$-manifolds with boundary whose groups of self-homotopy-equivalences are not finitely-generated.References
- Seymour Bachmuth and Horace Y. Mochizuki, $E_{2}\not =\textrm {SL}_{2}$ for most Laurent polynomial rings, Amer. J. Math. 104 (1982), no. 6, 1181–1189. MR 681732, DOI 10.2307/2374056
- A. M. Brunner and J. G. Ratcliffe, Finite $2$-complexes with infinitely-generated groups of self-homotopy-equivalences, Proc. Amer. Math. Soc. 86 (1982), no. 3, 525–530. MR 671229, DOI 10.1090/S0002-9939-1982-0671229-1
- David Frank and Donald W. Kahn, Finite complexes with infinitely-generated groups of self-equivalences, Topology 16 (1977), no. 2, 189–192. MR 478140, DOI 10.1016/0040-9383(77)90019-2
- John Kalliongis, Homotopy equivalences on nonirreducible $3$-manifolds, Indiana Univ. Math. J. 32 (1983), no. 6, 903–915. MR 721572, DOI 10.1512/iumj.1983.32.32062
- Darryl McCullough, Finite aspherical complexes with infinitely-generated groups of self-homotopy-equivalences, Proc. Amer. Math. Soc. 80 (1980), no. 2, 337–340. MR 577770, DOI 10.1090/S0002-9939-1980-0577770-2
- Robert Riley, An elliptical path from parabolic representations to hyperbolic structures, Topology of low-dimensional manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977) Lecture Notes in Math., vol. 722, Springer, Berlin, 1979, pp. 99–133. MR 547459
- Dennis Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269–331 (1978). MR 646078, DOI 10.1007/BF02684341 W. Thurston, The geometry and topology of three-manifolds, mimeographed notes, Princeton University.
- Friedhelm Waldhausen, Gruppen mit Zentrum und $3$-dimensionale Mannigfaltigkeiten, Topology 6 (1967), 505–517 (German). MR 236930, DOI 10.1016/0040-9383(67)90008-0
- Clarence W. Wilkerson, Applications of minimal simplicial groups, Topology 15 (1976), no. 2, 111–130. MR 402737, DOI 10.1016/0040-9383(76)90001-X
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 625-629
- MSC: Primary 55P10; Secondary 57M99
- DOI: https://doi.org/10.1090/S0002-9939-1984-0746102-2
- MathSciNet review: 746102