Related papers: Are large distance Heegaard splittings generic ?

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…

We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{g_1,\ldots,g_n\}\subset G$ is universal, i.e if the closure $\overline{<\mathcal{S}>}$ is equal to $G$, where $G$ is either the special unitary or the…

This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…

We describe the generic singularity of a Schubert variety of type A on each irreducible component of its singular locus. This singularity is given either by a cone of rank one matrices, or a quadratic cone.

The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…

A set $I$ is said to be a universal indifferent set for $1$-genericity if for every $1$-generic $G$ and for all $X \subseteq I$, $G \Delta X$ is also $1$-generic. Miller showed that there is no infinite universal indifferent set for…

We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…

We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\mathbb{P}^r$. In this…

We show that if the Hempel distance of a Heegaard splitting is larger than three then the mapping class group of the Heegaard splitting is isomorphic to a subgroup of the mapping class group of the ambient 3-manifold. This implies that…

We prove that the infinitesimal variations of Hodge structure arising in a number of geometric situations are non-generic. In particular, we consider the case of generic hypersurfaces in complete smooth projective toric varieties, generic…

In this paper, we show that, for any integers $n\geq 2$ and $g\geq 2$, there exist genus-$g$ Heegaard splittings of compact 3-manifolds with distance exactly $n$.

We show that after one stabilization, a strongly irreducible Heegaard splitting of suitably large genus of a graph manifold is isotopic to an amalgamation along a modified version of the system of canonical tori in the JSJ decomposition. As…

We investigate Birkhoff genericity on submanifolds of homogeneous space $X=SL_d(\bR)\ltimes (\bR^d)^k/ SL_d(\bZ)\ltimes (\bZ^d)^k$, where $d\geq 2$ and $k\geq 1$ are fixed integers. The submanifolds we consider are parameterized by unstable…

A gap in a paper of Rubinstein-Scharlemann is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in the original paper are not…

In 2001, J. Hempel proved the existence of Heegaard splittings of arbitrarily high distance by using a high power of a pseudo-Anosov map as the gluing map between two handlebodies. We show that lower bounds on distance can also be obtained…

In this paper, we show that, for each non-trivial two bridge knot K and for each g > 2, every genus g Heegaard splitting of the exterior E(K) of K is reducible.

J Hempel [Topology, 2001] showed that the set of distances of the Heegaard splittings (S,V, h^n(V)) is unbounded, as long as the stable and unstable laminations of h avoid the closure of V in PML(S). Here h is a pseudo-Anosov homeomorphism…

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the…

We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column distances of a convolutional code. We establish some…