Tangential equivalence of group actions
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- by Sławomir Kwasik PDF
- Trans. Amer. Math. Soc. 283 (1984), 563-573 Request permission
Abstract:
We consider the problem of tangential equivalence of group actions on manifolds. In particular we discuss a conjecture of B. Mazur and its modifications. The negative answer to this conjecture is presented. On the other hand we prove that the "isovariant" version of this conjecture, as well as the modified one, remains true. As an application some results on the tangential equivalence of ${Z_p}$-actions on homotopy spheres are obtained.References
-
A. Assadi, Finite group actions on simply-connected manifolds and $CW$ complexes, Mem. Amer. Math. Soc. No. 257 (1982).
- Glen E. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46, Academic Press, New York-London, 1972. MR 0413144
- Sören Illman, Smooth equivariant triangulations of $G$-manifolds for $G$ a finite group, Math. Ann. 233 (1978), no. 3, 199–220. MR 500993, DOI 10.1007/BF01405351
- I. M. James and G. B. Segal, On equivariant homotopy type, Topology 17 (1978), no. 3, 267–272. MR 508889, DOI 10.1016/0040-9383(78)90030-7
- Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR 148075, DOI 10.1090/S0273-0979-2015-01504-1 S. Lang, L’equivalence homotopique tangentielle, Séminaire Bourbaki 1960/61, Exp. 217-222.
- R. Lashof and M. Rothenberg, $G$-smoothing theory, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 211–266. MR 520506
- Peter Löffler, Homotopielineare $Z_{p}$-Operationen auf Sphären, Topology 20 (1981), no. 3, 291–312 (German). MR 608602, DOI 10.1016/0040-9383(81)90004-5
- Barry Mazur, Stable equivalence of differentiable manifolds, Bull. Amer. Math. Soc. 67 (1961), 377–384. MR 130697, DOI 10.1090/S0002-9904-1961-10626-5
- Barry Mazur, The method of infinite repetition in pure topology. I, Ann. of Math. (2) 80 (1964), 201–226. MR 169224, DOI 10.2307/1970391
- Barry Mazur, The method of infinite repetition in pure topology. II. Stable applications, Ann. of Math. (2) 83 (1966), 387–401. MR 196758, DOI 10.2307/1970474
- J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358–426. MR 196736, DOI 10.1090/S0002-9904-1966-11484-2
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Mel Rothenberg, Torsion invariants and finite transformation groups, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 267–311. MR 520507
- Anne Scott, Infinite regular neighborhoods, J. London Math. Soc. 42 (1967), 245–253. MR 212807, DOI 10.1112/jlms/s1-42.1.245
- L. C. Siebenmann, On detecting open collars, Trans. Amer. Math. Soc. 142 (1969), 201–227. MR 246301, DOI 10.1090/S0002-9947-1969-0246301-9
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 283 (1984), 563-573
- MSC: Primary 57S15; Secondary 57S17
- DOI: https://doi.org/10.1090/S0002-9947-1984-0737884-9
- MathSciNet review: 737884