Decompositions of 3-manifolds and pseudo-isotopies

Voxman, William

doi:10.1090/S0002-9947-1972-0293608-5

Decompositions of $3$-manifolds and pseudo-isotopies
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Trans. Amer. Math. Soc. 164 (1972), 503-508 Request permission

Abstract:

In this paper we construct pseudo-isotopies which realize certain cellular decompositions of 3-manifolds. In general we show that the pseudo-isotopy may be defined so as to leave points fixed outside of a given open set containing the nondegenerate elements of the decomposition. For nondegenerately continuous decompositions it is shown that the pseudo-isotopy does not move the nondegenerate elements far from their original positions.

References

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T. M. Price, Decompositions of $S^{3}$ and pseudo-isotopies, Trans. Amer. Math. Soc. 140 (1969), 295–299. MR 242136, DOI 10.1090/S0002-9947-1969-0242136-1

Approximating cellular maps by homeomorphisms

17

On the shrinkability of decompositions of

manifolds

William L. Voxman, On the shrinkability of decompositions of $3$-manifolds, Trans. Amer. Math. Soc. 150 (1970), 27–39. MR 261577, DOI 10.1090/S0002-9947-1970-0261577-8
William Voxman, Nondegenerately continuous decompositions of $3$-manifolds, Fund. Math. 68 (1970), 307–320. MR 273588, DOI 10.4064/fm-68-3-307-320
William Voxman, On the union of certain cellular decompositions of $3$-manifolds, Illinois J. Math. 15 (1971), 387–392. MR 281179