Related papers: A survey on Seifert fiber space conjecture

We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.

We prove Simon's conjecture for 3-manifolds.

This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey…

General considerations on the Equivalence conjectures and a review of few mathematical results.

We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.

We extend the original cylinder conjecture on point sets in affine three-dimensional space to the more general framework of divisible linear codes over $\mathbb{F}_q$ and their classification. Through a mix of linear programming,…

We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an…

We establish an inequality which gives strong restrictions on when the standard definite plumbing intersection lattice of a Seifert fibered space over $S^2$ can embed into a standard diagonal lattice, and give two applications. First, we…

In this paper, we confirm a conjecture of Orlik-Randell from 1977 on the Seifert form of chain type invertible singularities. We use Lefschetz bifibration techniques as developed by Seidel (inspired by Arnold and Donaldson) and take…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

The notion of generalized Seifert fibration is introduced, it is shown that the projections of certain Eschenburg $7$-manifolds onto ${\mathbb C} P^2$ define such fibrations, and for them the characteristic classes corresponding to the…

Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…

We present a reduction of the Hilbert-Smith conjecture in the case of the finite dimensional orbit space to some algebraic topology problems.

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

In this paper the circulant Hadamard conjecture is proved.

We show that the decision problem of recognising whether a triangulated 3-manifold admits a Seifert fibered structure with non-empty boundary is in NP. We also show that the problem of producing Seifert data for a triangulation of such a…

We survey progress on the Kakeya conjecture in Euclidean space, with an emphasis on developments that have occurred since the previous surveys by Wolff and Katz-Tao.

We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.

Theory of motivic superpolynomials is developed, including its extension to algebraic links colored by rows, relations to $L$-functions of plane curve singularities, the justification of the motivic versions of Weak Riemann Hypothesis, and…