On the action of $\Theta ^{n}$. I
HTML articles powered by AMS MathViewer
- by H. E. Winkelnkemper PDF
- Trans. Amer. Math. Soc. 206 (1975), 339-346 Request permission
Abstract:
We prove two theorems about the inertia groups of closed, smooth, simply-connected $n$-manifolds. Theorem A shows that, in certain dimensions, the special inertia group, unlike the full inertia group, can never be equal to ${\Theta ^n}$; Theorem B shows, in $\operatorname {dimensions} \equiv 3\bmod 4$, how to construct explicit closed $n$-manifolds ${M^n}$ such that $\Theta (\partial \pi )$ is contained in the inertia group of ${M^n}$.References
- William Browder, On the action of $\Theta ^{n}\,(\partial \pi )$, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 23–36. MR 0179799
- E. H. Brown Jr. and B. Steer, A note on Stiefel manifolds, Amer. J. Math. 87 (1965), 215–217. MR 175137, DOI 10.2307/2373232
- Samuel Gitler and James D. Stasheff, The first exotic class of $BF$, Topology 4 (1965), 257–266. MR 180985, DOI 10.1016/0040-9383(65)90010-8 R. Lashof, Theorems of Browder and Novikov, mimeographed notes, Univ. of Chicago, 1965.
- 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
- V. A. Rohlin, New results in the theory of four-dimensional manifolds, Doklady Akad. Nauk SSSR (N.S.) 84 (1952), 221–224 (Russian). MR 0052101 D. Sullivan, Smoothing homotopy equivalences, mimeographed notes, Univ. of Warwick, 1966. —, Triangulating homotopy equivalences, Thesis, Princeton University, 1965.
- Itiro Tamura, Sur les sommes connexes de certaines variétés différentiables, C. R. Acad. Sci. Paris 255 (1962), 3104–3106 (French). MR 143221 H. E. Winkelnkemper, Equators of manifolds and the action of ${\Theta ^n}$, Thesis, Princeton University, 1970.
- H. E. Winkelnkemper, Manifolds as open books, Bull. Amer. Math. Soc. 79 (1973), 45–51. MR 310912, DOI 10.1090/S0002-9904-1973-13085-X
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 206 (1975), 339-346
- MSC: Primary 57D60
- DOI: https://doi.org/10.1090/S0002-9947-1975-0413136-6
- MathSciNet review: 0413136