|
Diffeomorphisms of manifolds with finite fundamental group
Author(s):
Georgia
Triantafillou
Journal:
Bull. Amer. Math. Soc.
31
(1994),
50-53.
MathSciNet review:
1249354
Retrieve article in:
PDF
Abstract |
References |
Additional information
Abstract:
We show that the group of pseudoisotopy classes of diffeomorphisms of a manifold of dimension and of finite fundamental group is commensurable to an arithmetic group. As a result is a group of finite type.
References:
-
- [B]
- W. Browder, Diffeomorphisms of 1-connected manifolds, Trans. Amer. Math. Soc. 128 (1967), 155-163. MR 0212816 (35:3681)
- [BH]
- A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485-535. MR 0147566 (26:5081)
- [BS]
- A. Borel and J. P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436-491. MR 0387495 (52:8337)
- [C]
- J. Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le theoréme de la pseudoisotopie, Publ. Math. Inst. Hautes Études Sci. 39 (1970).
- [DDK]
- E. Dror, W. Dwyer, and D. Kan, Self homotopy equivalences of virtually nilpotent spaces, Comment. Math. Helv. 56 (1981), 599-614. MR 656214 (84h:55005)
- [H]
- A. Hatcher, A proof of a Smale conjecture, Ann. of Math. (2) 117 (1983), 553-607. MR 701256 (85c:57008)
- [HW]
- A. Hatcher and J. Wagoner, Pseudo-isotopies of compact manifolds, Asterisque 6 (1973). MR 0353337 (50:5821)
- [HS]
- W. C. Hsiang and R. Sharpe, Parametrized surgery and isotopy, Pacific J. Math. 67 (1976), 401-459. MR 0494165 (58:13091)
- [I]
- K. Igusa, What happens to Hatcher and Wagoner's formula for
when the first Postnikov invariant of M is nontrivial?, Lecture Notes in Math., vol. 1046, Springer-Verlag, New York, 1984, pp. 104-172. MR 750679 (86a:57026) - [KM]
- M. Kervaire and J. Milnor, Groups of homotopy spheres. I, Ann. of Math. 2 (1963), 504-537. MR 0148075 (26:5584)
- [Sm]
- S. Smale, Diffeomorphisms of the 2-sphere, Proc. Amer. Math. Soc. 10 (1969), 621-626. MR 0112149 (22:3004)
- [S]
- D. Sullivan, Infinitesimal computations in topology, Publ. Math. Inst. Hautes Études Sci. 47 (1978), 269-331. MR 0646078 (58:31119)
- [Tu]
- E. Turner, Diffeomorphisms of a product of spheres, Invent. Math. 8 (1969), 69-82. MR 0250323 (40:3562)
- [W]
- C. Wilkerson, Minimal simplicial groups, Topology 15 (1976), 111-130. MR 0402737 (53:6551)
Additional Information:
DOI:
10.1090/S0273-0979-1994-00496-3
PII:
S 0273-0979(1994)00496-3
Keywords:
Diffeomorphism,
isotopy,
arithmetic group,
homotopy equivalence
Copyright of article:
Copyright
1994,
American Mathematical Society
|