Topology Seminar

The homotopy type of the fiber of the $p^\text{th}$ power map on loop spaces of spheres

Steven Amelotte, University of Rochester

Wednesday, October 3rd, 2018
5:00 PM - 6:00 PM
Hylan 1106A

In this talk, I will describe the problem of decomposing the homotopy fiber of the $p^\text{th}$ power map on loop spaces of spheres as a product of indecomposable factors. In particular, I will outline a proof that, for odd primes $p$, the decomposition problem for $\Omega S^{2n+1}\{p\}$ is equivalent to the strong odd primary Kervaire invariant problem. Time permitting, I will discuss relations to other classical problems in homotopy theory concerning homotopy exponents, Moore spaces, the double suspension map and the Kahn–Priddy theorem.

Event contact: samelott at ur dot rochester dot edu