Mathematics – Algebraic Topology
Scientific paper
2012-04-23
Mathematics
Algebraic Topology
12 pages
Scientific paper
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. There are also various lower estimates for TC(X) such as the nilpotency of the ring $H^*(X\times X,\Delta(X))$, and the weak and stable topological compexity wTC(X) and $\sigma$TC(X). In general the difference between these upper and lower bounds can be arbitrarily large. In this paper we investigate spaces whose topological complexity is close to the maximal value given by Farber's formula and show that in these cases the gap between the lower and upper bounds is narrow and that TC(X) often coincides with the lower bounds. In addition, we show that the fibrewise definitions of TC and TC^M given by Iwase in Sakai coincide if X is a finite simplicial complex.
Franc Aleksandra
Pavešić Petar
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