Spaces with high topological complexity

作者：Franc Aleksandra^*; Pavesic Petar

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2014, 144(4): 761-773.

DOI：10.1017/S030821051200087X

By a formula of Farber, the topological complexity TC(X) of a (p - 1)-connected m-dimensional CW-complex X is bounded above by (2m + 1)/p + 1. We show that the same result holds for the monoidal topological complexity TCM(X). In a previous paper we introduced various lower bounds for TCM(X), such as the nilpotency of the ring H*(X x X, Delta(X)), and the weak and stable (monoidal) topological complexity wTC(M)(X) and sigma TCM(X). In general, the difference between these upper and lower bounds can be arbitrarily large. In this paper we investigate spaces with topological complexity close to the maximal value given by Farber's formula. We show that in these cases the gap between the lower and upper bounds is narrow and TC(X) often coincides with the lower bounds.

• 出版日期2014-8