Vol. 74, No. 2, 1978

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Super triangulations

R. H. Bing and Michael Peter Starbird

Vol. 74 (1978), No. 2, 307–325

This paper concerns itself with continuous families of linear embeddings of triangulated complexes into E2. In [2] Cairns showed that if f and g are two linear embeddings of a triangulated complex (C,T) into E2 so that there is an orientation preserving homeomorphism k of E2 with k f = g, then there is a continuous family of linear embeddings ht: (C,T) E2(t [0,1]) so that h0 = f and h1 = g. In this paper we prove various relative versions of this result when C is an arc, a 𝜃-curve, or a disk.

Mathematical Subject Classification
Primary: 57C35, 57C35
Received: 13 April 1977
Published: 1 February 1978
R. H. Bing
Michael Peter Starbird