U. Haifa Topology & Geometry seminar: Sunday, Apr. 3, 2022. Speaker: Sanjeevi Krishnan (Ohio State University). Title: “A Kan Condition for Directed Homotopy”.
Time: 17:00 (Israel Time)
Location: On Zoom
Abstract.
The Kan condition guarantees that a simplicial set, a formal colimit of abstract simplices, models enough features of a topological space so that classical homotopy theory can be given a completely combinatorial description. There is a similar such Kan condition for cubical sets, formal colimits of abstract hypercubes. We present a generalization of the Kan condition suitable for directed homotopy theory, a homotopy theory for spaces with direction (like spacetimes). Concretely, we present a lifting condition on cubical sets, satisfied by all nerves of small categories, that yields a cubical approximation theorem for directed topology. Intuitively, this condition can be regarded as some kind of weak higher categorical structure on a cubical set. A distinguishing feature of the lifting condition is that it is an algebraic lifting condition [Garner, Grandis, Riehl] in the sense that the lifts have to be suitably natural. One simple application is a cochain-theoretic description of a directed $1$-cohomology theory, represented by directed classifying spaces of commutative monoids.
ZOOM COORDINATES:
https://us02web.zoom.us/j/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09
Meeting ID: 849 8759 1026
Future speakers:
Niles Johnson (OSU) – April 10th
Surojit Ghosh (IIT Roorkee) – April 24th
Dimitri Ara (Marseilles) – May 1st
Sourav Das (Haifa) – May 8th
Viktoriya Ozornova (Bonn) – May 15th
Andrew Salch (Wayne State) – May 22nd
Markus Upmeier (Aberdeen) – May 29th
Denis-Charles Cisinski (Regensburg) – June 5th.
