Topological complexity of motion planning and Massey products

Mark Grant¹
Banach Center Publ. 85 (2009), 193-203
doi:10.4064/bc85-0-14

Abstract: 
We employ Massey products to find sharper lower
 bounds for the Schwarz genus of a fibration than those previously known. In particular we give examples of non-formal spaces
$X$ for which the topological complexity ${\bf TC}(X)$ (defined to be the genus of the free path fibration on $X$) is greater than the
zero-divisors cup-length plus one.

MSC (2000): Primary 55M99, 55S30; Secondary 68T40.
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