Mathematical Sciences Research Institute

Home » Workshop » Schedules » A Knot Floer Stable Homotopy Type

A Knot Floer Stable Homotopy Type

[HYBRID WORKSHOP] Floer Homotopical Methods in Low Dimensional and Symplectic Topology November 14, 2022 - November 18, 2022

November 17, 2022 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Ciprian Manolescu (Stanford University)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

A Knot Floer Stable Homotopy Type


Given a grid diagram for a knot or link K in the three-sphere, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions. (This is joint work with Sucharit Sarkar.)

Asset no preview A Knot Floer Stable Homotopy Type 606 KB application/pdf Download
Video/Audio Files

A Knot Floer Stable Homotopy Type

Troubles with video?

Please report video problems to itsupport@msri.org.

See more of our Streaming videos on our main VMath Videos page.