Related papers: A Fueter operator for 3/2-spinors
We define a variant of the Seiberg-Witten equations using the Rarita-Schwinger operators for closed simply connected spin smooth 4-manifold X. The moduli space of solutions to the system of non-linear differential equations consist of…
This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a…
Motivated by a conjecture of Donaldson and Segal, we take a first step towards defining a new 3-manifold Floer theory, where the complex is defined by a count of Fueter sections of a hyperk\"ahler bundle over the 3-manifold with fibers…
We discuss a 4[k/2]-dimensional complete hyperk\"ahler submanifold of the (4k-4)-dimensional moduli space of strongly centred SU(2)-monopoles of charge k.
We prove that a sequence of Fueter sections of a bundle of compact hyperkahler manifolds $\mathfrak X$ over a $3$-manifold $M$ with bounded energy converges (after passing to a subsequence) outside a $1$-dimensional closed rectifiable…
Motivated by a conjecture of Donaldson and Segal on the counts of monopoles and special Lagrangians in Calabi-Yau 3-folds, we prove a compactness theorem for Fueter sections of charge 2 monopole bundles over 3-manifolds: Let $u_k$ be a…
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 solutions $\mathcal{M}$ can be non-compact due to the appearance…
We study the moduli space of solutions to the Seiberg-Witten equations with $N$ spinors on a compact Riemann surface. These moduli spaces arise in a program to define a new enumerative invariant of 3-manifolds. They are also of independent…
A $\mathbb Z_2$-harmonic spinor on a 3-manifold $Y$ is a solution of the Dirac equation on a bundle that is twisted around a submanifold $\mathcal Z$ of codimension 2 called the singular set. This article investigates the local structure of…
Let $\mathcal{Z}$ be a spin $4$-manifold carrying a parallel spinor and $M\hookrightarrow \mathcal{Z}$ a hypersurface. The second fundamental form of the embedding induces a flat metric connection on $TM$. Such flat connections satisfy a…
We consider a variant of the Seiberg-Witten equations for multiple-spinors. The moduli space of solutions to our generalized Seiberg-Witten equations in the setting of K\"ahler surfaces has a direct relation with ASD connections of…
We consider the moduli space MN of flat unitary connections on an open Kaehler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection and L2 cohomologies with…
In this paper, we study the Seiberg-Witten equations on a compact 3-manifold with boundary. Solutions to these equations are called monopoles. Under some simple topological assumptions, we show that the solution space of all monopoles is a…
We produce new non-K\"ahler, non-Einstein, complete expanding gradient Ricci solitons with conical asymptotics and underlying manifold of the form $\R^2 \times M_2 \times \cdots \times M_r$, where $r \geq 2$ and $M_i$ are arbitrary closed…
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 equations are typically non-compact. We construct Kuranishi…
Starting from Joyce's generalised Kummer construction, we exhibit non-trivial families of $\mathrm{G}_2$-manifolds over the two dimensional sphere by resolving singularities with a twisted family of Eguchi-Hanson spaces. We establish that…
It is known that the almost-Kaehler anti-self-dual metrics on a given 4-manifold sweep out an open subset in the moduli space of anti-self-dual metrics. However, we show here by example that this subset is not generally closed, and so need…
The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of 2-dimensional sigma models as…
In this note, we propose an extension of the relation between worldsheet global symmetries and structures over moduli spaces of superconformal field theories (SCFTs) to include noninvertible symmetries. The most familiar examples of such…
A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of…