MSc Mathematics Pre-thesis Seminar
Date: Thursday, 9 November 2023
Time: 3.45 - 4.45 PM
Venue: Lecture Hall 202
Topics in Stable Homotopy Theory
Advait Phadnis
Chennai Mathematical Institute.
09-11-23

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Abstract

We know that $\pi_n(S^n)=\mathbb{Z}$ for all $n\geq1$ and $\pi_m(S^n)=\{1\}$ whenever $mn$? Stable homotopy groups provide a tool to understand the groups $\pi_m(\Sigma^n{X})$ for ``large" values of $m$ and $n$ and the patterns that emerge within them. This talk will be a brief overview of the more basic results in Stable Homotopy Theory including Freudenthal Suspension Theorem and Brown Representability. We will see how an attempt to study the category of reduced cohomology theories very naturally gives rise to the study of spectra. Prerequisites: An understanding of (pointed) topological spaces and some basic concepts from category theory.