## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**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.

**Date:** Monday, November 10, 1997

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Ran Levi

**Contact email:** ran@math.nwu.edu

**Contact Phone:** 847-467-1634

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Department of Mathematics, Northwestern University.