Deformations of group actions

Edmonds, Allan L.

doi:10.1090/S0002-9947-1975-0362321-0

Deformations of group actions

Author: Allan L. Edmonds
Journal: Trans. Amer. Math. Soc. 201 (1975), 147-160
MSC: Primary 57C25; Secondary 57E25
DOI: https://doi.org/10.1090/S0002-9947-1975-0362321-0
MathSciNet review: 0362321
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite group and be a compact piecewise linear (PL) manifold. Define a PL -isotopy to be a level-preserving PL action of on $M \times [0,1]$ . In this paper PL -isotopies are studied and PL -isotopic actions (which need not be equivalent) are characterized.

[1] R. H. Bing, A homeomorphism between the -sphere and the sum of two solid homed spheres, Ann. of Math. (2) 56 (1952), 354-362. MR 14, 192. MR 0049549 (14:192d)
[2] G. Bredon, Introduction to compact transformation groups, Academic Press, New York, 1972. MR 0413144 (54:1265)
[3] R. Connelly, A new proof of Brown's collaring theorem, Proc. Amer. Math. Soc. 27 (1971), 180-182. MR 42 #2490. MR 0267588 (42:2490)
[4] M. Curtis, Cartesian products with intervals, Proc. Amer. Math. Soc. 12 (1961), 819-820. MR 23 #A3582. MR 0126286 (23:A3582)
[5] A. Edmonds, Deformations of group actions, Bull. Amer. Math. Soc. 79 (1973), 1254-1257. MR 0331413 (48:9746)
[6] -, Local connectedness of spaces of finite group actions (to appear).
[7] J. F. P. Hudson, Piecewise linear topology, Benjamin, New York, 1969. MR 40 #2094. MR 0248844 (40:2094)
[8] L. Jones, The converse to the fixed point theorem of P. A. Smith. I, Ann. of Math. (2) 94 (1971), 52-68. MR 45 #4427. MR 0295361 (45:4427)
[9] M. Kervaire, Le théorème de Barden-Mazur-Stallings, Comment. Math. Helv. 40 (1965), 31-42. MR 32 #6475. MR 0189048 (32:6475)
[10] J. Milnor, Some free actions of cyclic groups on spheres, Differential Analysis Bombay Colloq. (1964), Oxford Univ. Press, London, 1964, pp. 37-42. MR 32 #6482. MR 0189055 (32:6482)
[11] R. Palais, Equivalence of nearby differentiable actions of a compact group, Bull. Amer. Math. Soc. 67 (1961), 362-364. MR 39 #3500. MR 0130321 (24:A185)
[12] R. Palais and T. Stewart, Deformations of compact differentiable transformation groups, Amer. J. Math. 82 (1960), 935-937. MR 22 #11401. MR 0120652 (22:11401)