Any 3-manifold 1-dominates at most finitely many 3-manifolds of -geometry

Any 3-manifold 1-dominates at most finitely many 3-manifolds supporting geometry.

     

All orientable 2-manifolds have finitely many minimal triangulations

We show that for every orientable 2-manifold there is a finite set of triangulations from which all other triangulations can be generated by sequences of vertex splittings.     

Minimal Euler characteristics of 4-manifolds with 3-manifold groups

Let π = π₁(M) for a compact 3-manifold M, and χ₄, p and q*be the invariants of Hausmann and Weinberger(1985), Kotschick(1994) and Hillman(2002), respectively. For a certain class of compact 3-manifolds M, including all those not containing two-sided RP2’s, we determine χ₄(π). We address when p(π)equals χ₄(π) and when q^*(π) equals χ₄(π), and answer a question raised by Hillman(2002).     

Contact 3-manifolds with infinitely many Stein fillings

Infinitely many contact 3-manifolds each admitting infinitely many pairwise non-diffeomorphic Stein fillings are constructed. We use Lefschetz fibrations in our constructions and compute their first homologies to distinguish the fillings.

     

Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation

We investigate group actions on simply-connected (second countable but not necessarily Hausdorff) 1-manifolds and describe an infinite family of closed hyperbolic 3-manifolds whose fundamental groups do not act nontrivially on such 1-manifolds. As a corollary we conclude that these 3-manifolds contain no Reebless foliation. In fact, these arguments extend to actions on oriented -order trees and hence these 3-manifolds contain no transversely oriented essential lamination; in particular, they are non-Haken.

     

A geometric classification of immersions of 3-manifolds into 5-space

In this paper we define two regular homotopy invariants c and i for immersions of oriented 3-manifolds into ⁵ in a geometric manner. The pair (c(f), i(f)) completely describes the regular homotopy class of the immersion f. The invariant i corresponds to the 3-dimensional obstruction that arises from Hirsch-Smale theory and extends the one defined in [10] for immersions with trivial normal bundle.Mathematics Subject Classification (2000): 57N35, 57R45, 57R42     

Any chart with at most one crossing is a ribbon chart

In this paper, we shall show the one written in the title.     

Commensurability of 1-cusped hyperbolic 3-manifolds

We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres where every commensurable knot complement in a homology sphere has non-monic Alexander polynomial.

     

Weighted approximation by entire functions interpolating at finitely or infinitely many points on the real line

We give error estimates for the weighted approximation of functions on the real line with Freud-type weights, by entire functions interpolating at finitely or infinitely many points on the real line. The error estimates involve weighted moduli of continuity corresponding to general Freud-type weights for which the density of polynomials is not always guaranteed.     

The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature

We investigate the limiting fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks with finitely many patterns at the critical temperature 1/β _c = 1. At the critical temperature, the measure-valued random variables given by the distribution of the appropriately scaled order parameter under the Gibbs measure converge weakly towards a random measure which is non-Gaussian in the sense that it is not given by a Dirac measure concentrated in a Gaussian distribution. This remains true in the case of β = β _N →β _c = 1 as N→∞ provided β _N converges to β _c = 1 fast enough, i.e., at speed ?(1/). The limiting distribution is explicitly given by its (random) density. Received: 12 May 1998 / Revised version: 14 October 1998     

Hyperbolic groups have flat-rank at most 1

The flat-rank of a totally disconnected, locally compact group G is an integer, which is an invariant of G as a topological group. We generalize the concept of hyperbolic groups to the topological context and show that a totally disconnected, locally compact, hyperbolic group has flat-rank at most 1. It follows that the simple totally disconnected locally compact groups constructed by Paulin and Haglund have flat-rank at most 1.     

Boundary structure of hyperbolic 3-manifolds admitting toroidal fillings at large distance

We show that if a hyperbolic 3-manifold M has two toroidal Dehn fillings with distance at least 3, then ∂M consists of at most three tori. As a result, we can obtain an optimal estimate for the number of exceptional slopes on hyperbolic 3-manifolds with boundary a union of at least 4 tori. S. Lee was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2007-314-C00024). M. Teragaito was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), 19540089.     

The π1 of self-maps of nonzero degree on 3-manifolds

Supported by NSFC and AvH     

Maximum principle at infinity for complete minimal surfaces in flat 3-manifolds

The main result of this paper is the following maximum principle at infinity:Theorem.Let M ₁ and M ₂ be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M ₁,M ₂)=min(dist(M ₁,M ₂), dist(M ₂,M ₁)).In case one boundary is empty, e.g. M ₁,then dist(M ₁,M ₂)=dist(M ₂,M ₁).If both boundaries are empty, then M ₁ and M ₂ are flat.