 
Summary: CURVATURE TESTING IN 3DIMENSIONAL
METRIC POLYHEDRAL COMPLEXES
MURRAY ELDER AND JON MCCAMMOND1
Abstract. In a previous article, the authors described an algorithm
to determine whether a finite metric polyhedral complex satisfied vari
ous local curvature conditions such as being locally CAT(0). The proof
made use of Tarski's theorem about the decidability of first order sen
tences over the reals in an essential way and thus was not immediately
applicable to a specific finite complex. In this article we describe an algo
rithm restricted to 3dimensional complexes which uses only elementary
3dimensional geometry. After describing the procedure we include sev
eral examples involving Euclidean tetrahedra which were run using an
implementation of the algorithm in GAP.
In this article we describe an algorithm to determine whether or not a
finite 3dimensional Mcomplex is locally CAT(). The procedure is based
purely on elementary 3dimensional geometry, and has considerable compu
tational advantages over the algorithm for Mcomplexes of arbitrary dimen
sion which was described by the authors in [6]. After describing the proce
dure we include several examples involving Euclidean tetrahedra which were
run using an implementation of the algorithm in GAP. The implementation
