Seminar series
Date
Thu, 31 Jan 2008
Time
11:00 -
12:00
Location
SR1
Speaker
Oscar Randal-Williams
Organisation
University of Oxford
For continuous maps $f: S^{2n-1} \to S^n$ one can define an integer-valued invariant, the so-called Hopf invariant. The problem of determining for which $n$ there are maps having Hopf invariant one can be related to many problems in topology and geometry, such as which spheres are parallelisable, which spheres are H-spaces (that is, have a product), and what are the division algebras over $\mathbb{R}$.
The best way to solve this problem is using complex K-theory and Adams operations. I will show how all the above problems are related, give an introduction to complex K-theory and it's operations, and show how to use it to solve this problem.