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Maps between orbifolds

Author: Masayuki Yamasaki
Journal: Proc. Amer. Math. Soc. 109 (1990), 223-232
MSC: Primary 57N80; Secondary 57M12
Erratum: Proc. Amer. Math. Soc. 115 (1992), null.
MathSciNet review: 1017853
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Abstract: Elementary homotopy theory on maps between orbifolds is discussed. For example, it is shown that, given a homomorphism $ \varphi $ between orbifold fundamental groups of certain orbifolds, there exists a map (unique up to homotopy) between the orbifolds which induces $ \varphi $. We also study the properties of orbifolds preserved by homotopy-equivalences.

References [Enhancements On Off] (What's this?)

  • [1] F. Connolly and T. Kozniewski, Classification of crystallographic manifolds with odd order holonomy, (preprint).
  • [2] M. W. Davis and J. W. Morgan, Finite group actions on homotopy $ 3$-spheres, The Smith Conjecture, Pure and Appl. Math. 112 (Bass and Morgan, eds.), Academic Press, Orlando, Florida, 1984, pp. 181-225. MR 758469
  • [3] S. Ferry, J. Rosenberg and S. Weinberger, Equivariant topological rigidity phenomena, C. R. Acad. Sci. Paris 306 I (1988), 777-782. MR 951234 (89f:57051)
  • [4] R. H. Fox, Covering spaces with singularities, Algebraic Geometry and Topology, Princeton Univ. Press, Princeton, New Jersey, 1957, pp. 243-257. MR 0123298 (23:A626)
  • [5] W. C. Hsiang and W. Pardon, When are topologically equivalent orthogonal representations equivalent?, Invent. Math. 68 (1982), 275-316. MR 666164 (84g:57037)
  • [6] M. Kato, On uniformizations of orbifolds, Homotopy Theory and Related Topics, Adv. Studies in Pure Math. 9 (H. Toda, ed.), Kinokuniya, Tokyo and North-Holland, Amsterdam, 1986, pp. 149-172. MR 896951 (89e:57035)
  • [7] I. Madsen and M. Rothenberg, Classifying $ G$-spheres, Bull. Amer. Math. Soc. 7 (1982), 223-226. MR 656199 (83h:57054)
  • [8] W. H. Meeks, III and S.-T. Yau, Group actions on $ {{\mathbf{R}}^3}$, The Smith Conjecture, Pure and Appl. Math. 112 (Bass and Morgan, eds.), Academic Press, Orlando, Florida, 1984, pp. 167-179.
  • [9] P. Scott, The geometries of $ 3$-manifolds, Bull. London Math. Soc. 15 (1983), 401-487. MR 705527 (84m:57009)
  • [10] Y. Takeuchi, A clssification of a class of $ 3$-branchfolds, Trans. Amer. Math. Soc. 307 (1988), 481-502. MR 940214 (89g:57018)
  • [11] -, Waldhausen's classification theorem for finitely uniformizable $ 3$-orbifolds, (preprint).
  • [12] W. Thurston, The geometry and topology of three manifolds, Lecture Notes, Dept. of Math., Princeton Univ., Princeton, NJ, (1976-1979).

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Keywords: Orbifold, orbi-map, tame map, OR-map
Article copyright: © Copyright 1990 American Mathematical Society

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