13 citations · 67 across the 11 of their papers we have counts for
5 papers · 1 filter
On counting associative submanifolds and Seiberg-Witten monopoles
Aleksander Doan, Thomas Walpuski
Building on ideas from [DT98; DS11; Wal17; Hay17], we outline a proposal for constructing Floer homology groups associated with a G2-manifold. These groups are generated by associa…
On the existence of harmonic spinors
Aleksander Doan, Thomas Walpuski
We prove the existence of singular harmonic spinors on -manifolds with . The proof relies on a wall-crossing formula for solutions to the Seiberg-Witten equ…
Deformation theory of the blown-up Seiberg-Witten equation in dimension three
Aleksander Doan, Thomas Walpuski
Associated with every quaternionic representation of a compact, connected Lie group there is a Seiberg-Witten equation in dimension three. The moduli spaces of solutions to these e…
Seiberg-Witten monopoles with multiple spinors on a surface times a circle
Aleksander Doan
The Seiberg-Witten equation with multiple spinors generalises the classical Seiberg-Witten equation in dimension three. In contrast to the classical case, the moduli space of solut…
Adiabatic limits and Kazdan-Warner equations
Aleksander Doan
We study the limiting behaviour of solutions to abelian vortex equations when the volume of the underlying Riemann surface grows to infinity. We prove that the solutions converge s…