26 citations · 49 across the 16 of their papers we have counts for
17 papers
Bloch Groups of Rings
Rodrigo Cuitun Coronado, Kevin Hutchinson
We give a definition of (refined) Bloch groups of general commutative rings which agrees with the standard definition in the case of local rings whose residue field has at least $4…
-rings and a graph of unimodular rows
Kevin Hutchinson
For a commutative ring we consider a related graph, , whose vertices are the unimodular rows of length up to multiplication by units. We prove that is path-con…
The Chern class for and the cyclic quantum dilogarithm
Kevin Hutchinson
In this note we confirm the conjecture of Calegari, Garoufalidis and Zagier in their recent paper in Ann. Sci. École Normale Sup. that , where is their map on $K_3…
The homology of of discrete valuation rings
Kevin Hutchinson, Behrooz Mirzaii, Fatemeh Yeganeh Mokari
Let be a discrete valuation ring with field of fractions and (sufficiently large) residue field . We prove that there is a natural exact sequence $H_3(\mathrm{SL}_2(A),\…
The third homology of
Kevin Hutchinson
We calculate the third homology of with half-integral coefficients. Corresponding to each prime there is an operator on this group with square the i…
Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system
Miguel D. Bustamante, Kevin Hutchinson, Yuri V. Lvov +1
In systems of N coupled anharmonic oscillators, exact resonant interactions play an important role in the energy exchange between normal modes. In the weakly nonlinear regime, thos…
Tate kernels, etale K-theory and the Gross kernel
Kevin Hutchinson
For an odd prime and a number field containing a th root of unity, we study generalised Tate kernels, , for and , having the prop…
The second homology of SL_2 of S-integers
Kevin Hutchinson
We calculate the structure of the finitely-generated groups H_2(SL_2(Z[1/m])) when m is a multiple of 6. We construct explicit homology classes which generate these groups and have…
Low-dimensional Homology of SL_2(k[t,1/t])
Kevin Hutchinson
We prove analogues of the fundamental theorem of algebraic K-theory for the second and third homology of SL_2 over an infinite field k. The statements involve Milnor-Witt K-theory…
The third homology of SL_2 of local rings
Kevin Hutchinson
We describe the third homology of SL_2 of local rings over Z[1/2] in terms of a refined Bloch group. We use this to derive a localization sequence for the third homology of SL_2 of…
On third homology of SL_2 and weak homotopy invariance
Kevin Hutchinson, Matthias Wendt
The goal of the paper is to achieve - in the special case of the linear group SL_2 - some understanding of the relation between group homology and its A^1-invariant replacement. We…
The third homology of SL_2 of fields with discrete valuation
Kevin Hutchinson
For a field F with discrete valuation and residue field we relate the third homology of SL_2(F) with half-integral coefficients to the third homology of SL_2(k) and a certain r…
A Bloch-Wigner complex for SL_2
Kevin Hutchinson
We introduce a refinement of the Bloch-Wigner complex of a field F. This is a complex of modules over the multiplicative group of the field. Instead of computing K_2 and indecompos…
Lines crossing a tetrahedron and the Bloch group
Kevin Hutchinson, Masha Vlasenko
We consider a simple modification of the Chow group CH^2(Spec(k),3) using only linear subvarieties in affine spaces and show that it maps surjectively to the Bloch group B(k) for a…
A refined Bloch group and the third homology of SL_2 of a field
Kevin Hutchinson
We use the properties of the refined Bloch group of a field to prove that H_3 of SL_2 of a global field is never finitely generated, and to calculate - up to some 2-torsion - H_3 o…
Homology stability for the special linear group of a field and Milnor-Witt K-theory
Kevin Hutchinson, Liqun Tao
Let F be a field of characteristic zero and let f(t,n) be the stabilization homomorphism from the n-th integral homology of SL(t,F) to the n-th homology of SL(t+1,F). We prove the…
The third homology of the special linear group of a field
Kevin Hutchinson, Liqun Tao
We prove that for any infinite field homology stability for the third integral homology of the special linear groups begins at . When the cokernel of the map f…