arXiv research

Study on tautness tensor for Riemannian foliations.

The study of smoothing arcs and curves on surfaces, proving tautness and arc length spectrum properties.

Generalizes Álvarez class vanishing to singular Riemannian foliations.

We define a norm on the homology of a foliated manifold, which refines and majorizes the usual Gromov norm on homology. This norm depends in an upper semi-continuous way on the underlying foliation, in the geometric topology, and can therefore be used to study the question of which foliations arise as geometric limits …

For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and oth…

Non-unimodular foliations have specific geometric properties.

The Euler class conjecture links geometric structures to integral points on the Thurston norm ball.

We continue the study of linear families of contact forms on 3-manifolds begun in our paper `Contact geometry and complex surfaces'. The present paper introduces Teichmuller and moduli spaces for so-called taut contact circles. By constructing a developing map for taut contact circles, we show that these geometrically …

We give an equivalent description of taut submanifolds of complete Riemannian manifolds as exactly those submanifolds whose normal exponential map has the property that every preimage of a point is a union of submanifolds. It turns out that every taut submanifold is also $\mathbb Z_2$-taut. We explicitely construct gen…

For a singular Riemannian foliation whose leaves are properly embedded, we show in the first part of this article the existence of global tubular neighbourhoods, and we develop a global description of the foliation as stratification by types of leaves. The second part deals with the further restriction to a foliation w…

Proves $PU(n,1)$ is 1-taut, concluding studies of rank-one Lie groups.

The number of Klein-bottle leaves in taut foliations is invariant under smooth deformations.

Tautness of submanifolds in spheres is preserved under Lie sphere transformations.

This paper concerns the problem of existence of taut foliations among 3-manifolds. Since the contribution of David Gabai, we know that closed 3-manifolds with non-trivial second homology group admit a taut foliations. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite di…

Essential loops found in taut ideal triangulations.

Taut foliations map leaves to branched 2-sphere covers.

Torus leaves play a crucial role in the theory of foliations. For example non-taut foliations admit a torus leaf (see the article of Goodman). In this paper, we study all the foliations near a torus leaf, and try to understand why sometimes it is taut, or non-taut (and Reebless). We focus on some crucial examples to un…

New results show how complex representations are needed to realize taut sutured handlebodies as homology products.

The state sums defining the quantum hyperbolic invariants (QHI) of hyperbolic oriented cusped $3$-manifolds can be split in a "symmetrization" factor and a "reduced" state sum. We show that these factors are invariants on their own, that we call "symmetry defects" and "reduced QHI", provided the manifolds are endowed w…

Proof of contact structure from taut foliation for certain knots.

3-manifolds with Heegaard 2 admit taut foliations if their fundamental group is left-orderable.

A taut ideal triangulation of a 3-manifold is a topological ideal triangulation with extra combinatorial structure: a choice of transverse orientation on each ideal 2-simplex, satisfying two simple conditions. The aim of this paper is to demonstrate that taut ideal triangulations are very common, and that their behavio…

Paper proves depth bounds for taut foliations using instanton Floer homology.

We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.

New findings on $L$-spaces and taut foliations in hyperbolic links.

Constructs taut foliations for surgeries on positive 3-braids, confirming L-space conjecture.

This is a short, elementary survey article about taut submanifolds. In order to simplify the exposition, we restrict to the case of compact smooth submanifolds of Euclidean or spherical spaces. Some new, partial results concerning taut 4-manifolds are discussed at the end of the text.

New foliations constructed from contact pairs, revealing flexible taut foliations.

Floer homology detects taut foliations in rational homology spheres.

Left orderability proven for certain 3-manifolds with specific foliations.

We introduce cosymplectic circles and cosymplectic spheres, which are the analogues in the cosymplectic setting of contact circles and contact spheres. We provide a complete classification of compact 3-manifolds that admit a cosymplectic circle. The properties of tautness and roundness for a cosymplectic $p$-sphere are…

Constructs taut branched surfaces from veering triangulations in hyperbolic 3-manifolds.

A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of …

In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness result of Haefliger can be obtained in our particular setting as a straightforward co…

Whitehead link surgeries are not L-spaces if they support taut foliations.

New triangulations encode flows with vanishing polynomial.

Finite quotients of fibered hyperbolic 3-manifold groups detect taut polynomials.

New foliations found in 3D spaces from positive braids.

Agol recently introduced the concept of a veering taut triangulation, which is a taut triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, givin…

This paper proves a converse to Thurston's 1976 observation for taut foliations on hyperbolic 3-manifolds.

Study positive braid knots and their taut foliations, proving some L-space conjecture evidence.

Developed algorithms to compute three polynomial invariants of veering triangulations.

We give a necessary and sufficient criterion for a sutured manifold to be taut in terms of the twisted homology of the sutured manifold.

The study proves estimates for transverse nonlinear equations on Sasakian manifolds with applications in geometry.

The Euler class of taut foliations on Dehn fillings is studied, leading to new left-orderable slopes.

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterizat…

We describe notions of tautness that arise in the study of $C^0$ foliations, $C^{1,0}$ or smoother foliations, and in geometry. We give examples to show that these notions are different, and discuss how these differences impact some classical foliation results. We construct examples of smoothly taut $C^{\infty,0}$ foli…

The Whitehead link exterior lacks most Euler class taut foliations.