Bounds in piecewise linear topology
L. B. Treybig · Transactions of the American Mathematical Society · 1975
The following types of results are obtained: Given a polyhedral 2 2 -sphere P P with rectilinear triangulation T T lying in the interior of a solid tetrahedron G G in E 3 {E^3} , then there is a simplicial isotopy f : G × [ 0 , 1 ] → G f:G \times [0,1] \to G taking P P onto a tetrahedron so that for t t in [ 0 , 1 ] , f ( x , t ) = x [0,1],f(x,t) = x on Bd ( G ) \text {Bd} (G) and f t {f_t} is affine on each element of the triangulation S S of G G , where card ( S ) (S) is a known function of card