-manifolds which admit finite group actions

Author:
Shi Cheng Wang

Journal:
Trans. Amer. Math. Soc. **339** (1993), 191-203

MSC:
Primary 57M60; Secondary 57M50, 57N10

DOI:
https://doi.org/10.1090/S0002-9947-1993-1169084-0

MathSciNet review:
1169084

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove several results which support the following conjectures: Any smooth action of a finite group on a geometric -manifold can be conjugated to preserve the geometric structure. Every irreducible closed -manifold with infinite is finitely covered by a Haken -manifold.

**[B]**G. Bredon,*Introduction to compact transformation group*, Academic Press, 1972. MR**0413144 (54:1265)****[BM]**H. Bass and J. Morgon,*The Smith conjecture*, Academic Press, 1984. MR**758459 (86i:57002)****[E]**A. L. Edmonds,*Transformation groups and low-dimensional manifolds*, Contemp. Math., vol. 36, Amer. Math. Soc., Providence, R.I., 1985, pp. 339-366. MR**780973 (86f:57033)****[G]**M. J. Greenberg,*Lectures on algebraic topology*, Benjamin, New York, 1967. MR**0215295 (35:6137)****[Ha]**J. Hass,*Surfaces minimizing area in their homology class and group action on*-*manifolds*, Math. Z.**199**(1988), 501-509. MR**968316 (90d:57017)****[H1]**J. Hempel, -*manifolds*, Ann. of Math. Studies, no. 86, Princeton Univ. Press, Princeton, N.J., 1976. MR**0415619 (54:3702)****[H2]**-,*Orientation reversing involutions and the first betti number for finite covering of*-*manifolds*, Invent. Math.**67**(1982), 133-143. MR**664329 (83m:57010)****[H3]**-,*Branch cover over strongly amphicheiral links*, Topology**29**(1990), 247-255. MR**1056273 (92b:57006)****[Ki]**T. H. Kiang,*The theory of fixed point classes*, Science Press, Beijing, 1979, 1986; English transl., Springer-Verlag, Berlin, Heidelberg, and New York, 1989. MR**1002187 (90h:55002)****[K]**S. Kojima,*Finite covers of*-*manifolds containing essential surfaces of Euler characteristic*, Proc. Amer. Math. Soc.**101**(1987), 743-748. MR**911044 (89b:57010)****[L]**J. Luecke,*Finite covers of*-*manifolds containing essential tori*, Trans. Amer. Math. Soc.**310**(1988), 371-381. MR**965759 (90c:57011)****[MS]**W. H. Meeks and P. Scott,*Finite group action on*-*manifolds*, Invent. Math.**86**(1986), 287-345. MR**856847 (88b:57039)****[MSY]**W. Meeks, L. Simon, and S. T. Yau,*Embedded minimal surfaces, exotic spheres and manifolds of positive Ricci curvature*, Ann. of Math. (2)**116**(1982), 621-659. MR**678484 (84f:53053)****[R]**D. Rolfsen,*Knots and links*, Publish or Perish, 1976. MR**0515288 (58:24236)****[S]**P. Scott,*The geometries of*-*manifolds*, Bull. London Math. Soc.**15**(1983), 401-487. MR**705527 (84m:57009)****[To]**J. L. Tollefson,*Involution of sufficiently large*-*manifolds*, Topology**20**(1981), 323-352. MR**617370 (82h:57014)****[T1]**W. Thurston,*Three dimensional manifolds, Kleinian groups and hyperbolic geometry*, Bull. Amer. Math. Soc. (N.S.)**7**(1983), 357-382. MR**648524 (83h:57019)****[T2]**-,*Geometry and topology on*-*manifolds*, preprint.**[T3]**-,*Three-manifolds with symmetry*, preprint.**[W1]**S. Wang,*Several results in*-*and*-*manifolds*, Thesis, UCLA, 1988.**[W2]**-,*The virtual*-*representibility of*-*manifolds which admit orientation reversing involution*, Proc. Amer. Math. Soc.**110**(1990), 497-501.

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
57M60,
57M50,
57N10

Retrieve articles in all journals with MSC: 57M60, 57M50, 57N10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1169084-0

Article copyright:
© Copyright 1993
American Mathematical Society