Related papers: Deformed $G_2$-instantons on $\mathbb{R}^4 \times …
This article consists of some loosely related remarks about the geometry of G_2-structures on 7-manifolds and is partly based on old unpublished joint work with two other people: F. Reese Harvey and Steven Altschuler. Much of this work has…
Let $E$ be a flat Lorentzian space of signature $(2, 1)$. A Margulis space-time is a noncompact complete Lorentz flat $3$-manifold $E/\Gamma$ with a free isometry group $\Gamma$ of rank $g \geq 2$. We consider the case when $\Gamma$…
Motivated by the S-duality conjecture, we study the Donaldson-Thomas invariants of the 2 dimensional Gieseker stable sheaves on a threefold. These sheaves are supported on the fibers of a nonsingular threefold X fibered over a nonsingular…
We prove that for a group $\mathrm{SO}_n(\mathrm{R}) \subset G \subset \mathrm{GL}_n (\mathrm{R})$, any $G$-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a…
We prove that energy minimizing Yang-Mills connections on a compact $G_{2}$-manifold has holonomy equal to $G_{2}$ are $G_{2}$-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing…
We introduce and study a notion of invariant intrinsic torsion geometry which appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S^3. This space is foliated by six-dimensional hypersurfaces, each…
This paper uses algebro-topological techniques such as characteristic classes and obstruction theory, together with the $h$-principles for $\widetilde{\mathrm{G}}_2$ and $\mathrm{SL}(3;\mathbb{R})^2$ forms recently established by the author…
We construct an obstruction for the existence of embeddings of homology $3$-sphere into homology $S^3\times S^1$ under some cohomological condition. The obstruction is defined as an element in the filtered version of the instanton Floer…
This paper is a short version of some joint work with Stefan Haller. It describes the structure of "smooth manifold with corners" on the space of possibly broken instantons and on the completion of unstable manifolds of a generic smooth…
We discuss general properties of strong G$_2$-structures with torsion and we investigate the twisted G$_2$ equation, which represents the G$_2$-analogue of the twisted Calabi-Yau equation for SU$(n)$-structures introduced by…
Motivated by $G_2$-manifolds with coassociative fibrations in the adiabatic limit, Donaldson and Scaduto conjectured the existence of associative submanifolds homeomorphic to a three-holed $3$-sphere with three asymptotically cylindrical…
Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative N=2 gauge theory; this construction is based on the generalized…
With the aim of investigating the existence of an integrable elliptic deformation of strings on $\mathsf{AdS}_3 \times \mathsf{S}^3 \times \mathsf{T}^4$, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic…
We construct SU(2)^2xU(1)-invariant G_2-instantons on the asymptotically conical limit of the C7 family of G_2-metrics. The construction uses a dynamical systems approach involving perturbations of an abelian solution and a solution on the…
We construct a variant of Floer homology groups and prove a gluing formula for a variant of Donaldson invariants. As a corollary, the variant of Donaldson invariants is non-trivial for connected sums of 4-manifolds which satisfy a condition…
Given a homomorphism $\tau$ from a suitable finite group $\mathsf{\Gamma}$ to $\mathsf{SU}(4)$ with image $\mathsf{\Gamma}^\tau$, we construct a cohomological gauge theory on a noncommutative resolution of the quotient singularity…
Supersymmetric configurations of type II D-branes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the kappa-symmetric worldvolume action. It is found in dimension four or…
We investigate Yang-Mills theories with arbitrary gauge group on $R^3\times S^1$, whose symmetry is spontaneously broken by the Wilson loop. We show that instantons are made of fundamental magnetic monopoles, each of which has a…
We discuss some new results on the construction of supersymmetric solutions of Type IIB supergravity of the form ${\rm WAdS}_3\times{\rm WS}^3\times T^4$, ${\rm WAdS}_3$ and ${\rm WS}^3$ denoting \emph{warped} anti-de Sitter spacetime and…
A deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a $G_2$-manifold $X$ satisfying a certain nonlinear PDE. This is considered to be the mirror of a (co)associative cycle in the context of…