Related papers: On embedding infinite cyclic covers in compact 3-m…

A closed totally geodesic surface in the figure eight knot complement remains incompressible in all but finitely many Dehn fillings. In this paper, we show that there is no universal upper bound on the number of such fillings, independent…

In this paper we give a proof of Lichnerowicz Conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the {\it Nice Embeddings} into eigen spaces of the Laplacian. Even if one wants to use these…

We prove the infinitesimal rigidity of some geometrically infinite hyperbolic 4- and 5-manifolds. These examples arise as infinite cyclic coverings of finite-volume hyperbolic manifolds obtained by colouring right-angled polytopes, already…

We show that the commutator subgroup G' of a classical knot group G need not have subgroups of every finite index, but it will if G' has a surjective homomorphism to the integers and we give an exact criterion for that to happen. We also…

We study the infinitesimal rigidity of equivariant minimal maps from the universal cover of a smooth oriented surface (possibly non-compact) into a Riemannian symmetric space, focusing on representations arising from cyclic harmonic…

We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R^3. We also provide examples of minimal vertex triangulations of closed, connected, orientable…

On the basis of a result of Barrett, we show that members of certain classes of abstract Levi flat manifolds with boundary, whose Levi foliation contains a compact leaf with contracting, flat holonomy, admit no $CR$ embedding as a…

We show that, for any prime p, a knot K in the 3-sphere is determined by its p-fold cyclic unbranched covering. We also investigate when the m-fold cyclic unbranched covering of a knot coincides with the n-fold cyclic unbranched covering of…

We obtain global extensions of the celebrated Nash-Kuiper theorem for $C^{1,\theta}$ isometric immersions of compact manifolds with optimal H\"older exponent. In particular for the Weyl problem of isometrically embedding a convex compact…

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is…

For any integer n > 2, the n-fold cyclic branched cover M of an alternating prime knot K in the 3-sphere determines K, meaning that if K is a knot in the 3-sphere that is not equivalent to K then its n-fold cyclic branched cover cannot be…

We prove that there is a second countable locally compact group that does not embed as a closed subgroup in any compactly generated locally compact group, and discuss various related embedding and non-embedding results.

We present a short proof of S. Parsa's theorem that there exists a compact $n$-polyhedron $P$, $n\ge 2$, non-embeddable in $\mathbb R^{2n}$, such that $P*P$ embeds in $\mathbb R^{4n+2}$. This proof can serve as a showcase for the use of…

We investigate nicely embedded H--holomorphic maps into stable Hamiltonian three--manifolds. In particular we prove that such maps locally foliate and satisfy a no--first--intersection property. Using the compactness results of…

In this paper, we show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic $3$-manifolds except some special cases.

In this paper, we show that any non-arithmetic hyperbolic $2$-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic $2$-bridge link complement cannot irregularly cover a hyperbolic $3$-manifold.…

We prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic…

We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient…

The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of $PL$ isometric embeddings of $PL$ compact surfaces into $\mathbb{R}^3$. We conclude that their proof does not admit a direct extension to…

We prove a version of Whitney's strong embedding theorem for isometric embeddings within the general setting of the Nash-Kuiper h-principle. More precisely, we show that any $n$-dimensional smooth compact manifold admits infinitely many…