New lower bounds for the topological complexity of aspherical spaces.

We show that the topological complexity of an aspherical space X is bounded below by the cohomological dimension of the direct product A × B , whenever A and B are subgroups of π 1 ( X ) whose conjugates intersect trivially. For instance, this assumption is satisfied whenever A and B are complementary subgroups of π 1 ( X ) . This gives computable lower bounds for the topological complexity of many groups of interest (including semidirect products, pure braid groups, certain link groups, and Higman's acyclic four-generator group), which in some cases improve upon the standard lower bounds in terms of zero-divisors cup-length. Our results illustrate an intimate relationship between the topological complexity of an aspherical space and the subgroup structure of its fundamental group. [ABSTRACT FROM AUTHOR]