Related papers: A new orbit closure in genus 8?

We study trisections of smooth, compact non-orientable 4-manifolds, and introduce trisections of non-orientable 4-manifolds with boundary. In particular, we prove a non-orientable analogue of a classical theorem of Laudenbach-Po\'enaru. As…

To date at least 10 highly flattened planes of dwarf galaxies are claimed to have been discovered in the Local Universe. The origin of these planes of galaxies remains unknown. One suggestion is that they are related to the large-scale…

In this paper we study the Grassmannian of submodules of a given dimension inside a finitely generated projective module $P$ for a finite dimensional algebra $\Lambda$ over an algebraically closed field. The orbit of such a submodule $C$…

We present a family of index 1 abelian current graphs whose derived embeddings can be modified into triangulations of $K_{12s}$ for $s \geq 4$. Our construction is significantly simpler than previous methods for finding genus embeddings of…

We show that there is a type-preserving homomorphism from the fundamental group of the figure-eight knot complement to the mapping class group of the thrice-punctured torus. As a corollary, we obtain infinitely many commensurability classes…

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…

We classify conjugacy classes of involutions in the isometry groups of nondegenerate, symmetric bilinear forms over the field of two elements. The new component of this work focuses on the case of an orthogonal form on an even dimensional…

We report the discovery of a dwarf planet candidate, 2017 OF201, currently located at a distance of 90 au. Its orbit is extremely wide and extends to the inner Oort cloud, with a semi-major axis of 830 au and a perihelion of 45 au,…

Whitehead doubles provide a plethora of examples of knots that are topologically slice but not smoothly slice. We discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used techniques to obstructing sliceness.…

Every GL(2,R)-orbit in hyperelliptic components of strata of abelian differentials in genus greater than two is either closed, dense, or contained in a locus of branched covers.

We present nine newly discovered globular clusters in the outer halo of M31, found by a semi-automated procedure from a INT Wide Field Camera survey of the region. The sample includes a candidate at the yet largest known projected…

Let $S_{g}$ denote the closed orientable surface of genus $g$. In joint work with Huang, the first author constructed exponentially-many (in $g$) mapping class group orbits of pairs of simple closed curves whose complement is a single…

We determine explicit orbit representatives of reducible Jordan algebras and of their corresponding Freudenthal triple systems. This work has direct application to the classification of extremal black hole solutions of N = 2, 4 locally…

We realize 4 of the 6 closed orientable flat 3-manifolds as a cusp section of an orientable finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps.

We study the relationship between pairs of topological dynamical systems $ (X,T) $ and $ (X',T') $, where $ (X',T') $ is the quotient of $ (X,T) $ under the action of a finite group $ G $. We describe three phenomena concerning the…

In this note, we point out an error in the proof of Theorem 4.7 of [P. Achar and A.~Henderson, `Orbit closures in the enhanced nilpotent cone', Adv. Math. 219 (2008), 27-62], a statement about the existence of affine pavings for fibres of a…

It is well known that an arbitrary closed orientable $3$-manifold can be realized as the unique boundary of a compact orientable $4$-manifold, that is, any closed orientable $3$-manifold is cobordant to zero. In this paper, we consider the…

We show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manifold bounds a surface of genus at most $g$ is in co-NP. This answers a question of Agol, Hass, and Thurston in 2002. Previously, this was…

This paper is devoted to the classification of GL^+(2,R)-orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of quadratic differentials. We show that the following dichotomy holds: an orbit is…

In this paper, we study the variety $Jor_{3}$ of three-dimensional Jordan algebras over the field of real numbers. We establish the list of $26$ non-isomorphic Jordan algebras and describe the irreducible components of $Jor_{3}$ proving…