EVENT DETAILS AND ABSTRACT

Title: Loop structures on homotopy fibres of self maps of a sphere
Speaker: Professor Ran Levi
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

Let $S^{2n-1}\{k\}$ denote the fibre of the degree $k$ map on the sphere $S^{2n-1}$. If $k=p^r$, where $p$ is an odd prime and $n$ divides $p-1$ then $S^{2n-1}\{k\}$ is known to be a loop space. It is also known that $S^3\{2^r\}$ is a loop space for $r\geq 3$. In this paper we study the possible loop structures on this family of spaces for all primes $p$. In particular we show that $S^3\{4\}$ is not a loop space. Our main result is that whenever $S^{2n-1}\{p^r\}$ i a loop space, the loop structure is unique up to homotopy.