Celebratio Mathematica — Kister — Complete Bibliography

Complete Bibliography

Works connected to R H Bing

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J. M. Kister: Isotopies in manifolds. Ph.D. thesis, University of Wisconsin, Madison, 1959. Advised by R. H. Bing. MR 2612903 phdthesis

R. H. Bing and J. M. Kister: “Taming complexes in hyperplanes,” Duke Math. J. 31 : 3 (1964), pp. 491–511. MR 0164329 Zbl 0124.16701 article

In this paper we investigate conditions that suffice for an imbedding of a complex in a Euclidean space to be tame. We also consider the more general question of when two imbeddings are equivalent. We show, for example, with a dimension restriction that if the image under an imbedding of a \( k \)-complex is contained in a hyperplane of codimension \( k \), then the imbedding is tame. More precisely we prove:

Let \( K \) be a finite \( k \)-dimensional complex and \( h \) an imbedding of \( K \) into an \( n \)-plane \( E^n \) in \( E^{n+k} \), where \( k+2\leq n \). Let \( \varepsilon \) be any positive number. Then there exists an isotopy \( G_t \) (\( t\in I \)) of \( E^{n+k} \) onto itself such that

\( g_0 \) is the identity,
\( g_1 h \) is piecewise linear,
\( g_t \) is the identity outside an \( \varepsilon \)-neighborhood of \( h(K) \) for each \( t \) in \( I \),
each point of \( E^{n+k} \) moves along a polygonal path under \( g_t \) (\( t\in I \)) having length less than \( \varepsilon \).

A. Blass and J. M. Kister: “Free subgroups of the homeomorphism group of the reals,” pp. 243–252 in Special volume in honor of R. H. Bing (1914–1986) (San Marcos, TX, November 1984), published as Topology Appl. 24 : 1–3. Issue edited by S. Singh and T. L. Thickstun. Elsevier (Amsterdam), December 1986. MR 872496 Zbl 0604.57015 incollection

R H Bing	Related	Volume
Sukhjit Singh	Related
Thomas Lusk Thickstun	Related
Andreas Raphael Blass	Related