WiSe 23/24 Oberseminar: The P¹-Freudenthal suspension theorem
Time and place: Tuesday 14:15-15:45 in M311 and online
The Freudenthal suspension theorem in homotopy theory states that the connectivity of the loop-suspension map X → ΩΣX is twice as high as the connectivity of X. In motivic homotopy theory, the algebraic projective line P¹ plays the role of the topological circle S¹, and the existence of a motivic version of the Freudenthal suspension theorem involving P¹ has been a natural open question since the beginning of motivic homotopy theory. It was recently resolved by Asok, Bachmann, and Hopkins. Among other applications, they obtain a proof of Murthy’s splitting conjecture on vector bundles of rank just below the dimension. In this seminar we will go through the proofs of the P¹-Freudenthal suspension theorem and of Murthy’s conjecture, following the paper:
- Aravind Asok, Tom Bachmann, Michael J. Hopkins, On P¹-stabilization in unstable motivic homotopy theory
| Date | Speaker | Topic |
|---|---|---|
| 24.10 | Marc Hoyois | Introduction and overview |
| 31.10 | Suraj Yadav | The A¹-connectivity theorem |
| 07.11 | Marco Giustetto | Nilpotent motivic spaces |
| 14.11 | Divya Ghanshani | Motivic spectra, t-structures and the slice filtration |
| 21.11 | Niklas Kipp | Real étale homotopy theory |
| 28.11 | Runlei Xiao | The homotopy coniveau tower |
| 05.12 | Giacomo Bertizzolo | Gₘ-delooping |
| 12.12 | Vova Sosnilo | Weak cellularity and nullification |
| 19.12 | Bastiaan Cnossen | Refined Whitehead theorem and towers |
| 09.01 | Timon Thanassis | The motivic Dold–Thom theorem |
| 16.01 | Pavel Sechin | Cellular estimates for Eilenberg–Mac Lane spaces |
| 23.01 | Marc Hoyois | The P¹-Freudenthal suspension theorem |
| 30.01 | Benjamin Dünzinger | Application to algebraic vector bundles |
| 06.02 |