Inertial $h$-cobordisms with finite cyclic fundamental group
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- by Terry C. Lawson
- Proc. Amer. Math. Soc. 44 (1974), 492-496
- DOI: https://doi.org/10.1090/S0002-9939-1974-0358820-2
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Abstract:
For $M$ a PL $n$-manifold, $n \geqq 5$, let $I(M)$ be the subset of torsions $\sigma \in \operatorname {Wh} ({\pi _1}M)$ such that the $h$-cobordism $W$ constructed from $M$ with torsion $\sigma$ has its other boundary component PL homeomorphic to $M$. We present three techniques dealing with the determination of $I(M)$ and apply them when ${\pi _1}M = {Z_q}$. We prove: (1) If $n$ is even, ${\pi _1}M \simeq {Z_q},q$ odd, then $I(M) = \operatorname {Wh} ({\pi _1}M)$. (2) If $n$ is odd, then there exists $M$ with ${\pi _1}M \simeq {Z_q}$ such that $I(M) = \operatorname {Wh} ({\pi _1}M)$.References
- A. Bak and W. Scharlau, Witt groups of orders and finite groups, 1972 (preprint).
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
- F. T. Farrell, The obstruction to fibering a manifold over a circle, Bull. Amer. Math. Soc. 73 (1967), 737–740. MR 215310, DOI 10.1090/S0002-9904-1967-11854-8
- V. K. A. M. Gugenheim, Some theorems on piecewise linear embedding, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 333–337. MR 48817, DOI 10.1073/pnas.38.4.333
- J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358–426. MR 196736, DOI 10.1090/S0002-9904-1966-11484-2
- Paul Olum, Self-equivalences of pseudo-projective planes. Simple equivalences, Topology 10 (1971), 257–260. MR 275428, DOI 10.1016/0040-9383(71)90009-7
- C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 492-496
- MSC: Primary 57D80; Secondary 57C10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0358820-2
- MathSciNet review: 0358820