The n-Category Café

Directed Homotopy at Liverpool

Posted by David Corfield

Zoran posted an announcement at the nForum for a EPSRC DTG studentship award for research leading to a PhD on the subject of Directed homotopy theory and $(\infty,1)$-categories at Liverpool University. There’s no mention of a deadline, but it begins very soon.

The work is to be supervised by Jon Woolf, who came to my attention during our discussion on fundamental $n$-categories with duals of statified spaces, back here. Subsequently, he wrote two papers Transversal homotopy theory and Whitney categories and the Tangle Hypothesis (with Conor Smyth) making rigorous the original Baez-Dolan idea.

Now hasn’t there got to be a connection to what Ayala and Rozenbluym are doing with sheaves over manifolds with stratified subcomplexes to reach $(\infty,n)$-categories with adjoints? Will it be a case again that $(\infty, n)$ proves simpler than plain $n$?

And what about Todd Trimble’s work on surface diagrams:

This study would involve a fascinating marriage between topics in pure higher category theory (n-categories with duals) and topics in pure differential topology (stratified Morse theory).

Stratification is in the air.