# Products of CW complexes

**Date**: Monday 30 October 2017, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Colloquia**Cost**: Free

#### Andrew Brooke-Taylor, University of Leeds. Part of the pure colloquia.

CW complexes are used extensively in algebraic topology as a suitable class of spaces to work with, general enough for most purposes while avoiding many irrelevant point-set topological pathologies. Dowker showed that the product (as topological spaces) of two CW complexes need not be a CW complex, but the question of when exactly the product of two CW complexes is a CW complex has remained open since Whitehead introduced them in the 1940's. After talking about the background and history of this problem, I will present a complete characterisation of when the product of two CW complexes is a CW complex.

Colloquia will be followed by a reception in the School of Maths common room.

**Andrew Brooke-Taylor**,* University of Leeds*