61 citations · 235 across the 22 of their papers we have counts for
23 papers
A 2-torsion invariant of 2-knots
Ryan Budney
In this paper we describe what should perhaps be called a `type-2' Vassiliev invariant of knots S^2 -> S^4. We give a formula for an invariant of 2-knots, taking values in Z_2 that…
Stabilisation, scanning and handle cancellation
Ryan Budney
In this note we describe a family of arguments that link the homotopy-type of a) the diffeomorphism group of the disc , b) the space of co-dimension one embedded spheres in a…
On the automorphism groups of hyperbolic manifolds
Ryan Budney, David Gabai
Let Diff(N) and Homeo(N) denote the smooth and topological group of automorphisms respectively that fix the boundary of the n-manifold N, pointwise. We show that the (n-4)-th homot…
Bi-filtrations and persistence paths for 2-Morse functions
Ryan Budney, Tomasz Kaczynski
This paper studies the homotopy-type of bi-filtrations of compact manifolds induced as the pre-image of filtrations of the plane for generic smooth functions f : M --> R^2. The pri…
Knotted 3-balls in S^4
Ryan Budney, David Gabai
The unknot U in S^4 has non-unique smooth spanning 3-balls up to isotopy fixing U. Equivalently there are properly embedded non-separating 3-balls in S^1xB^3 not properly isotopic…
High-Dimensional Classification for Brain Decoding
Nicole Croteau, Farouk S. Nathoo, Jiguo Cao +1
Brain decoding involves the determination of a subject's cognitive state or an associated stimulus from functional neuroimaging data measuring brain activity. In this setting the c…