Maps between orbifolds

Author:
Masayuki Yamasaki

Journal:
Proc. Amer. Math. Soc. **109** (1990), 223-232

MSC:
Primary 57N80; Secondary 57M12

DOI:
https://doi.org/10.1090/S0002-9939-1990-1017853-2

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 between orbifold fundamental groups of certain orbifolds, there exists a map (unique up to homotopy) between the orbifolds which induces . We also study the properties of orbifolds preserved by homotopy-equivalences.

**[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**-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**-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*, 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**-manifolds*, Bull. London Math. Soc.**15**(1983), 401-487. MR**705527 (84m:57009)****[10]**Y. Takeuchi,*A clssification of a class of**-branchfolds*, Trans. Amer. Math. Soc.**307**(1988), 481-502. MR**940214 (89g:57018)****[11]**-,*Waldhausen's classification theorem for finitely uniformizable**-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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1017853-2

Keywords:
Orbifold,
orbi-map,
tame map,
OR-map

Article copyright:
© Copyright 1990
American Mathematical Society