Diffeomorphisms of manifolds with finite fundamental group

Triantafillou, Georgia

doi:10.1090/S0273-0979-1994-00496-3

Diffeomorphisms of manifolds with finite fundamental group
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Bull. Amer. Math. Soc. 31 (1994), 50-53 Request permission

Abstract:

We show that the group $\mathcal {D}(M)$ of pseudoisotopy classes of diffeomorphisms of a manifold of dimension $\geq 5$ and of finite fundamental group is commensurable to an arithmetic group. As a result ${\pi _0}(Diff M)$ is a group of finite type.

References

William Browder, Diffeomorphisms of $1$-connected manifolds, Trans. Amer. Math. Soc. 128 (1967), 155–163. MR 212816, DOI 10.1090/S0002-9947-1967-0212816-0
Armand Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535. MR 147566, DOI 10.2307/1970210
A. Borel and J.-P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436–491. MR 387495, DOI 10.1007/BF02566134

La stratification naturelle des espaces de fonctions différentiables réelles et le theoréme de la pseudoisotopie

39

E. Dror, W. G. Dwyer, and D. M. Kan, Self-homotopy equivalences of virtually nilpotent spaces, Comment. Math. Helv. 56 (1981), no. 4, 599–614. MR 656214, DOI 10.1007/BF02566229
Allen E. Hatcher, A proof of the Smale conjecture, $\textrm {Diff}(S^{3})\simeq \textrm {O}(4)$, Ann. of Math. (2) 117 (1983), no. 3, 553–607. MR 701256, DOI 10.2307/2007035
Allen Hatcher and John Wagoner, Pseudo-isotopies of compact manifolds, Astérisque, No. 6, Société Mathématique de France, Paris, 1973. With English and French prefaces. MR 0353337
W. C. Hsiang and R. W. Sharpe, Parametrized surgery and isotopy, Pacific J. Math. 67 (1976), no. 2, 401–459. MR 494165, DOI 10.2140/pjm.1976.67.401
Kiyoshi Igusa, What happens to Hatcher and Wagoner’s formulas for $\pi _{0}C(M)$ when the first Postnikov invariant of $M$ is nontrivial?, Algebraic $K$-theory, number theory, geometry and analysis (Bielefeld, 1982) Lecture Notes in Math., vol. 1046, Springer, Berlin, 1984, pp. 104–172. MR 750679, DOI 10.1007/BFb0072020
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
Stephen Smale, Diffeomorphisms of the $2$-sphere, Proc. Amer. Math. Soc. 10 (1959), 621–626. MR 112149, DOI 10.1090/S0002-9939-1959-0112149-8
Dennis Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269–331 (1978). MR 646078, DOI 10.1007/BF02684341
Edward C. Turner, Diffeomorphisms of a product of spheres, Invent. Math. 8 (1969), 69–82. MR 250323, DOI 10.1007/BF01418871
Clarence W. Wilkerson, Applications of minimal simplicial groups, Topology 15 (1976), no. 2, 111–130. MR 402737, DOI 10.1016/0040-9383(76)90001-X