Related papers: Left orderability and taut foliations with one-sid…

In this paper, we define the recurrence and "non-wandering" for decompositions. The following inclusion relations hold for codimension one foliations on closed $3$-manifolds: $\{$minimal$\} \sqcup \{$compact$\}$ $\subsetneq$ $\{$pointwise…

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple…

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

We give an algorithmic proof of the theorem that a closed orientable irreducible and atoroidal 3-manifold has only finitely many Heegaard splittings in each genus, up to isotopy. The proof gives an algorithm to determine the Heegaard genus…

Let $X$ be an $(n+1)$-dimensional manifold, $\Delta$ be a one-dimensional foliation on $X$, and $p: X \to X / \Delta$ be a quotient map. We will say that a leaf $\omega$ of $\Delta$ is special whenever the space of leaves $X / \Delta$ is…

A k-submanifold L of an open n-manifold M is called weakly integrable (WI) [resp. strongly integrable (SI)] if there exists a submersion \Phi:M\to R^{n-k} such that L\subset \Phi^{-1}(0) [resp. L= \Phi^{-1}(0)]. In this work we study the…

We produce examples of taut foliations of hyperbolic 3-manifolds which are R-covered but not uniform --- ie the leaf space of the universal cover is R, but pairs of leaves are not contained in bounded neighborhoods of each other. This…

We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…

The main result of this paper is that for every closed, connected, orientable, irreducible 3-manifold $M$, there is an integer $ n_M$ such that any abstract graph with no automorphism of order 2 which has a 3-connected minor whose genus is…

We show that if $P$ is a $PD_3$-complex and $g\in\pi_1(P)$ has finite order $>1$ and infinite centraliser then $\pi_1(P)$ retracts onto $Z/2Z\oplus\mathbb{Z}$. If $P$ is an irreducible closed 3-manifold then it follows from the Projective…

Let N be an irreducible, compact 3-manifold with empty or toroidal boundary which is not a closed graph manifold. Using recent work of Agol, Kahn-Markovic and Przytycki-Wise we will show that pi_1(N) admits a cofinal filtration with `fast'…

We study taut foliations on the complements of non-split positive braid closures in $S^3$. If $L$ is such a link with components $L_1,\ldots,L_n$ and at least one component is not the unknot, then the Dehn surgery along a multislope…

A (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space $\mathbb{R}^3$ with transition maps in the affine transformation group $\mathrm{Aff}(\mathbb{R}^3)$. We will show that a connected closed affine…

In this paper, we study affine manifolds endowed with linear foliations. These are foliations defined by vector subspaces invariant by the linear holonomy. We show that an $n$-dimensional compact, complete, and oriented affine manifold…

In this paper we study the left-orderability of $3$-manifold groups using an enhancement, called recalibration, of Calegari and Dunfield's "flipping" construction, used for modifying $\mbox{Homeo}_+(S^1)$-representations of the fundamental…

We give an elementary proof of the fact that any orientable 3-manifold admits a framing (i.e. is parallelizable) and any non-orientable 3-manifold admits a projective framing. The proof uses only basic facts about immersions of surfaces in…

We show that for a closed $n$-manifold $N$ admitting a quasiregular mapping from the Euclidean $n$-space the following are equivalent: (1) order of growth of $\pi_1(N)$ is $n$, (2) $N$ is aspherical, and (3) $\pi_1(N)$ is virtually…

We prove that a topological manifold (possibly with boundary) admitting a continuous cancellative binary operation is orientable. This implies that the M\"obius band admits no cancellative continuous binary operation. This answers a…

Generalizing Heegaard splittings of 3-manifolds and trisections of 4-manifolds, we consider multisections of higher-dimensional smooth (or PL) closed orientable manifolds, namely decompositions into 1-handlebodies whose subcollections…

It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable…