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The P^1-Freudenthal suspension theorem SemesterWiSe 2023 / 24 Lecturer Marc Hoyois, Pavel Sechin Type of course (Veranstaltungsart) Oberseminar German title Der P^1-Freudenthalsche Einhängungssatz Contents The Freundenthal suspension theorem in homotopy theory states that the connectivity of the loop-suspension map X -> Loop(Susp X) is twice as high as the connectivity of X. In motivic homotopy theory, the algebraic projective line P^1 plays the role of the topological circle S^1, and the existence of a motivic version of the Freudenthal suspension theorem involving P^1 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 P^1-Freudenthal suspension theorem and of Murthy's conjecture. Literature Aravind Asok, Tom Bachmann, Michael J. Hopkins, On P^1-stabilization in unstable motivic homotopy theory Time/Date Di 14-16 Location tba Course homepage https://hoyois.app.uni-regensburg.de/WS24/freudenthal/index.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
MV, MSem ECTS 4,5 |