## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** On 2-local finite complexes and v_2-self-maps

**Speaker:** Philip Egger

**Speaker Info:** Northwestern

**Brief Description:** Thesis defense

**Special Note**:

**Abstract:**

A common method for finding large-scale periodic phenomena in
the p-local homotopy groups of spheres involves finding finite CW
complexes with self-maps that are non-nilpotent. Devinatz, Hopkins and
Smith gave a systematic way of finding complexes admitting self-maps that
are isomorphisms under Morava K-theory K(n)_*, known as v_n-self-maps.
However, finding the periodicity of the resulting phenomena in the
homotopy groups of spheres is hard.
In joint work with Bhattacharya and Mahowald, we consider the case n=p=2
and establish the periodicity of the v_2-self-maps on 8-cell complexes
A_1[ij] for i,j\in\{0,1\}. We then construct a 32-cell complex Z whose
v_2-self-map we hope will have lower periodicity.

**Date:** Monday, April 18, 2016

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. John Francis

**Contact email:** jnkf@math.northwestern.edu

**Contact Phone:** 847-491-5544

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