arXiv research

Corrects errors in previous studies on metric measure spaces.

Corrects errors in Hans' pseudocovering spaces paper.

In this paper, we develop new techniques for understanding surfaces in $\mathbb{CP}^2$ via bridge trisections. Trisections are a novel approach to smooth 4-manifold topology, introduced by Gay and Kirby, that provide an avenue to apply 3-dimensional tools to 4-dimensional problems. Meier and Zupan subsequently develope…

We correct a mistake on the citation of JSJ theory in \cite{Ni}. Some arguments in \cite{Ni} are also slightly modified accordingly.

We introduce the notions of geometric height and graded (geometric) relative hyperbolicity in this paper. We use these to characterize quasiconvexity in hyperbolic groups, relative quasiconvexity in relatively hyperbolic groups, and convex cocompactness in mapping class groups and $Out(F_n)$. Corrigendum: there is an u…

This note corrects an error in the char(K)=2 case of the author's computation of the bordism groups of K-Witt spaces for the field K.

In this note, we give the correct statements of [2,Proposition 3.3 and Theorem 3.4] and a formula of the Chern curvature in terms of the curvature tensor $R^V$ of the affine connection $\nabla^V$ and the Chern tensor $P$.

The purpose of this article is to point out a mistake in the published paper "Graphs of hyperbolic groups and limit set intersection theorem- Proc AMS, vol 146, no 5, pp 1859--1871, which subsequently weakens the main theorem of that paper. We state and prove a weaker result in this note.

A previous paper of the authors' contained an error in the proof of a key claim, that Rasmussen's knot-invariant s(K) is equal to its gauge-theory counterpart. The original paper is included here together with a corrigendum, indicating which parts still stand and which do not. In particular, the gauge-theory counterpar…

Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of Karpelevich-Mostow theorem. We also include a short discussion of the ori…

It is well-known that a point $T\in cv_N$ in the (unprojectivized) Culler-Vogtmann Outer space $cv_N$ is uniquely determined by its \emph{translation length function} $||.||_T:F_N\to\mathbb R$. A subset $S$ of a free group $F_N$ is called \emph{spectrally rigid} if, whenever $T,T'\in cv_N$ are such that $||g||_T=||g||_…

The proof of Theorem 7.12 of "Uniqueness of smooth cohomology theories" by the authors of this note is not correct. The said theorem identifies the flat part of a differential extension of a generalized cohomology theory E with ER/Z (there called "smooth extension"). In this note, we give a correct proof. Moreover, we …

The aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [13, 23] in the so--called $G-$framework…

New metrics found on homogeneous spaces, preserving key geometric properties.

Corrected and improved simulation methods for Dirichlet-Laplace prior.

We introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with rays that identify the "hyperbolic directions" in that space. This boundary is a quasi-isometry invariant and thus produces a well-defined boundary for any finitely generated group. In the case of a prope…