Related papers: Twisted-Austere Submanifolds in Euclidean Space

The configuration manifold $M$ of a mechanical system consisting of two unconstrained rigid bodies in $\mathbb{R}^n$, $n\geq 1$, is a manifold with boundary (typically with singularities.) A complete description of the system requires…

Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used. Suppose $M$ is a triangulated, compact, irreducible, boundary-irreducible 3-manifold. In Q-theory,…

Every compact 3-Sasakian 7-manifold $M$ admits a canonical 2-parameter family of co-closed $\text{G}_2$-structures $\varphi_{a,b}$ for $a,b > 0$, as well as a foliation by $\varphi_{a,b}$-associative 3-folds whose leaf space $X$ is a…

We derive formulas for the mean curvature of special Lagrangian 3-folds in the general case where the ambient 6-manifold has intrinsic torsion. Consequently, we are able to characterize those SU(3)-structures for which every special…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

A smooth closed 3-manifold $M$ fibered by tori $T^2$ is characterized by an element $\phi \in GL(2,\mathbb{Z})$. We show that $M$ is the boundary of a 4-manifold fibered by tori over a surface such that the bundle structure on $M$ is the…

In this paper, we complete the classification of which compact 3-manifolds have a virtually compact special fundamental group by addressing the case of mixed 3-manifolds. A compact aspherical 3-manifold is mixed if has at least one JSJ…

The twisted Alexander polynomials of a space, associated to a linear representation $\sigma$ of the fundamental group, are non-abelian refinements of the classical Alexander polynomial from knot theory. In this paper, we show that they…

We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be hermitian Yang-Mills, and also…

We show that the $D=11$ Supermembrane theory (M2-brane) compactified on a $M_9 \times T^2$ target space, with constant fluxes $C_{\pm}$ naturally incorporates the geometrical structure of a twisted torus. We extend the M2-brane theory to a…

Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as…

Following Ghomi and Tabachnikov we study topological obstructions to totally skew embeddings of a smooth manifold M in Euclidean spaces. This problem is naturally related to the question of estimating the geometric dimension of the stable…

A (bounded) manifold of circular type is a complex manifold M of dimension n admitting a (bounded) exhaustive real function u, defined on M minus a point x_o, so that: a) it is a smooth solution on $M\setminus {x_o}$ to the Monge-Amp\`ere…

For any integer $k$ we construct an explicit example of a twistor space which contains a one--parameter family of jumping rational curves, where the normal bundle changes from $O(1)+O(1)$ to $O(k)+O(2-k)$. For $k>3$ the resulting…

Suppose $K$ is an unknot lying in the 1-skeleton of a triangulated 3-manifold with $t$ tetrahedra. Hass and Lagarias showed there is an upper bound, depending only on $t$, for the minimal number of elementary moves to untangle $K$. We give…

We study polystable Higgs bundles twisted by a line bundle over a compact K\"ahler manifold. These form a Tannakian category when the first and second Chern classes of the bundle are zero. In this paper we identify the corresponding Tannaka…

Let $M$ be a $3$-manifold with connected non-vacuos boundary which is not spherical. Assume that $N$ is another $3$-manifold with vacuous boundary and $N^{\ast}$ is the $3$-manifold obtained by removing from $N$ the interior of a $3$-cell.…

We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)\times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models…

Using a combination of Atiyah-Segal ideas on one side and of Connes and Baum-Connes ideas on the other, we prove that the Twisted geometric K-homology groups of a Lie groupoid have an external multiplicative structure extending hence the…

In this paper, we analyze the geometric structure of an Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is…