Related papers: Real Slices of ${\rm SL}(r,\mathbb{C})$-Opers

In this paper we study manifolds, $X_{\Sigma}$, with fibred singularities, more specifically, a relevant space ${\mathcal R}^{\rm psc}(X_{\Sigma})$ of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the…

We define Wick-rotations by considering pseudo-Riemannian manifolds as real slices of a holomorphic Riemannian manifold. From a frame bundle viewpoint Wick-rotations between different pseudo-Riemannian spaces can then be studied through…

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not…

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an…

Motivated by the Lawrence-Krammer-Bigelow representations of the classical braid groups, we study the homology of unordered configurations in an orientable genus-$g$ surface with one boundary component, over non-commutative local systems…

We extend the notion of regularized integrals introduced by Li-Zhou that aims to assign finite values to divergent integrals on configuration spaces of Riemann surfaces. We then give cohomological formulations for the extended notion using…

Topologically, a compact Riemann surface $X$ of genus $g$ is a $g$-holed torus (a sphere with $g$ handles). This paper is an introduction to the theory of compact Riemann surfaces and algebraic curves. It presents the basic ideas and…

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar…

Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication…

We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin$^c$-Dirac operators, invariant under actions by possibly noncompact groups, with possibly noncompact orbit…

We prove results about orbit closures and equidistribution for the SL(2,R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure…

Let $\mathcal F$ be a holomorphic one-dimensional foliation on $\mathbb{P}^n$ such that the components of its singular locus $\Sigma$ are curves $C_i$ and points $p_j$. We determine the number of $p_j$, counted with multiplicities, in terms…

Let G = Z2 act on a finitistic space X having mod 2 cohomology of the product of three spheres S^n x S^m x S^l. In this paper, we have determined the fixed point sets of involutions on X. This generalizes J. C. Su [12] results for…

We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and…

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…

Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…

We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…

Let $\Omega$ be an unbounded two dimensional strip on a ruled surface in $\mathbb{R}^d$, $d\geq2$. Consider the Laplacian operator in $\Omega$ with Dirichlet and Neumann boundary conditions on opposite sides of $\Omega$. We prove some…

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction…

We study superdifferential operators of order $2n+1$ which are covariant with respect to superconformal changes of coordinates on a compact super Riemann surface. We show that all such operators arise from super M\"obius covariant ones. A…