Title: More stable stems
Speaker: Dan Isaksen
Speaker Info: Wayne State University
I will describe a joint project with Guozhen Wang and Zhouli Xu to compute stable homotopy groups at the prime 2.Date: Monday, October 10, 2016
The cofiber of tau is a curious motivic spectrum that allows us to combine information from the Adams spectral sequence and from the Adams-Novikov spectral sequence in ways that were previously not possible. The story begins with the surprising observation that the Adams spectral sequence for the cofiber of tau is the same as the algebraic Novikov spectral sequence. These spectral sequences have been computed by machine in a large range.
From this information about the Adams spectral sequence for the cofiber of tau, we can deduce information about the Adams spectral sequence for the sphere by passing to the top and bottom cells.
This method yields almost the entire structure of the Adams spectral sequence in a large range. It makes the computation of the first 60 stems essentially routine. So far, we have extended computations to the 70 stem, with ongoing progress into higher stems.