February 9
Andrew Brooke-Taylor,
University of Leeds
Products of CW complexes
CW complexes are the topological spaces of choice for algebraic topology, but the product (as topological spaces) of two CW complexes need not be a CW complex. In the 1940s and 50s Whitehead and Milnor gave sufficient conditions for the product to be a CW complex, and in the 70s and 80s Liu and Tanaka gave characterisations of those pairs of CW complexes whose product is a CW complex, under the assumption of set-theoretic axioms such as CH. In this talk I will present a new characterisation of the pairs of CW complexes whose product is a CW complex, valid in any model of set theory (ie, without any such extra set-theoretic assumptions). Whilst I have stripped the set theory away from the assumptions on the universe, the characterisation is with reference to a cardinal that may not be familiar to non-set theorists: the bounding number.