We examine the " homotopy coniveau tower " for a general cohomology theory on smooth k-schemes and give a new proof that the layers of this tower for K-theory agree with motivic cohomology. In addition, the homotopy coniveau tower agrees with Voevodsky's slice tower for S 1-spectra, giving a proof of a connect-edness conjecture of Voevodsky. The homotopy coniveau tower construction extends to a...

The main results of this article are certain connections between braid groups and the homotopy groups of the 2-sphere. The connections are given in terms of Brunnian braids over the disk and over the 2-sphere. The techniques arise from the natural structure of simplicial and ∆-structures on fundamental groups of configuration spaces.

For a compact Lie group G with maximal torus T, Pittie and Smith showed that the flag variety G/T is always a stably framed boundary. We generalize this to the category of p-compact groups, where the geometric argument is replaced by a homotopy theoretic argument showing that the class in the stable homotopy groups of spheres represented by G/T is trivial, even G-equivariantly. As an applicatio...

Abstract This paper deals with certain results on the number of smooth structures quaternionic projective spaces, obtained through computation inertia groups and their analogues, which in turn are computed using techniques from stable homotopy theory. We show that concordance group is trivial dimension 20, but there many examples high dimensions where non-trivial. extend these to computations c...

We prove that for n ≥ 1 and q > 0 the (oriented) cobordism group of fold maps of (oriented) (n + q)-dimensional manifolds into R contains the direct sum of ⌊(q + 1)/2⌋ copies of the (n − 1)th stable homotopy group of spheres as a direct summand. We also prove that for k ≥ 1 and q = 2k − 1 the cobordism group of fold maps of unoriented (n+ q)-dimensional manifolds into R also contains the nth st...