9 citations · 19 across the 6 of their papers we have counts for
9 papers
Existence of mASD connections on 4-manifolds with cylindrical ends
David L. Duncan, Ian Hambleton
Taubes' gluing theorems establish the existence of ASD connections on closed, oriented 4-manifolds. We extend these gluing results to the mASD connections of Morgan-Mrowka-Ruberman…
Characterizing immutable sandpiles: A first look
David L. Duncan, Wesley J. Engelbrecht
By working with coefficients in or , one can define two different notions of stability for a sandpile on a graph. We call a sandpile immutable when these n…
Critical group structure from the parameters of a strongly regular graph
Joshua E. Ducey, David L. Duncan, Wesley J. Engelbrecht +4
We give simple arithmetic conditions that force the Sylow -subgroup of the critical group of a strongly regular graph to take a specific form. These conditions depend only on th…
The Chern-Simons invariants for the double of a compression body
David L. Duncan
Given a 3-manifold that can be written as the double of a compression body, we compute the Chern-Simons critical values for arbitrary compact connected structure groups. We also sh…
The Yang-Mills flow for cylindrical end 4-manifolds
David L. Duncan
We establish various existence and uniqueness results for the Yang-Mills flow on cylindrical end 4-manifolds. We also show long-time existence and infinite-time convergence under c…
On the components of the gauge group for PU(r)-bundles
David L. Duncan
We discuss a general procedure for using characteristic classes to study the components of the gauge group for a principal G-bundle. To illustrate this, we work out the case where…
Higher-rank instanton cohomology and the quilted Atiyah-Floer conjecture
David L. Duncan
Given a closed, connected, oriented 3-manifold with positive first Betti number, one can define an instanton Floer group as well as a quilted Lagrangian Floer group. The quilted At…
An index relation for the quilted Atiyah-Floer conjecture
David L. Duncan
Given a closed, connected, oriented 3-manifold with positive first Betti number, one can define an instanton Floer group as well as a quilted Lagrangian Floer group. Each of these…
Compactness results for neck-stretching limits of instantons
David L. Duncan
We prove that, under a suitable degeneration of the metric, instantons converge to holomorphic quilts. To prove the main results, we develop estimates for the Yang-Mills heat flow…