Super triangulations

R. H. Bing and Michael Peter Starbird

Vol. 74 (1978), No. 2, 307–325

DOI: 10.2140/pjm.1978.74.307

Abstract

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 h_t: (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

Milestones

Received: 13 April 1977

Published: 1 February 1978