TOPOLOGICAL COMPLEXITY (WITHIN 1) OF THE SPACE OF ISOMETRY CLASSES OF PLANAR n-GONS FOR SUFFICIENTLY LARGE n

摘要

Hausmann and Rodriguez classified spaces of isometry classes of planar n-gons according to their genetic code which is a collection of sets (called genes) containing n. Omitting the n yields what we call gees. We prove that, for a set of gees with largest gee of size k > 0, the topological complexity (TC) of the associated space of n-gons is either 2n -5 or 2n-6 if n≥ 2k +3. We present evidence that suggests that it is very rare that the TC is not equal to 2n-5 or 2n - 6.