Michael A. Hill
The Equivariant Slice Filtration: a Primer.
Wed, 07/20/2011 - 15:01 — SomNambulAuthors: Michael A. Hill
Subjects: Algebraic Topology
AbstractWe present an introduction to the equivariant slice filtration. After
reviewing the definitions and basic properties, we determine the slice
dimension of various families of naturally arising spectra. This leads to an
analysis of pullbacks of slices defined on quotient groups, producing new
collections of slices. Building on this, we determine the slice tower for the
Eilenberg-Mac Lane spectrum associated to a Mackey functor for a cyclic
$p$-group. We then relate the Postnikov tower to the slice tower for various
spectra.On the non-existence of elements of Kervaire invariant one.
Thu, 08/27/2009 - 13:23 — SomNambulAuthors: Michael A. Hill, Michael J. Hopkins, Douglas C. Ravenel
Subjects: Algebraic Topology
AbstractWe show that Kervaire invariant one elements in the homotopy groups of
spheres exist only in dimensions at most 126. By Browder's Theorem, this means
that smooth framed manifolds of Kervaire invariant one exist only in dimensions
2, 6, 14, 30, 62, and possibly 126. With the exception of dimension 126 this
resolves a longstanding problem in algebraic topology.
User login
