What’s so special about cubes? (A Blakers-Massey theorem for non-cubical diagrams)

24/01/2020, 14:00 - 15:00 in MAP/0G/014

Taggart, Niall (Queen’s University Belfast)


Abstract:

The classical Blakers-Massey Theorem (and its dual) are theorems which directly compare (homotopy) pushout squares and (homotopy) pullback squares, giving an indication of to what degree a (homotopy) pullback square is a (homotopy) pushout and vice versa. Several groups of authors (Barratt-Whitehead, Ellis-Steiner, Brown-Loday, Goodwillie, Munson,…) generalised these results to similar results for higher dimensional cubes. These generalised results unify many classical results, and lie at the heart of calculus of functors, which has applications in algebraic and geometric topology.

In this talk, we will start from the classical Blakers-Massey theorem and discuss how this theorem generalises to higher dimensional cubes. The final part of this talk will be dedicated to answering the question “what’s so special about cubes?”, were we will provide a version of Blakers-Massey for non-cubical diagrams. This is joing work with Greg Arone.

Mathematical Sciences Research Centre