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Register a new userMaps from 3-manifolds to 4-manifolds that induce isomorphisms on $pi_1$
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In this paper, we prove that any closed orientable 3-manifold $M$ other than $#^k S^1times S^2$ and $S^3$ satisfies the following properties: (1) For any compact orientable 4-manifold $N$ bounded by $M$, the inclusion does not induce an isomorphism on their fundamental groups $pi_1$. (2) For any map $f:Mto N$ from $M$ to a closed orientable 4-manifold $N$, $f$ does not induce an isomorphism on $pi_1$. Relevant results on higher dimensional manifolds are also obtained.
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We produce a rational homology 3-sphere that does not smoothly bound either a positive or negative definite 4-manifold. Such a 3-manifold necessarily cannot be rational homology cobordant to a Seifert fibered space or any 3-manifold obtained by Dehn surgery on a knot. The proof requires an analysis of short characteristic covectors in bimodular lattices.
In this article we show that every closed orientable smooth $4$--manifold admits a smooth embedding in the complex projective $3$--space.
Let $M$ be a closed orientable irreducible $3$-manifold with a left orderable fundamental group, and $M_0 = M - Int(B^{3})$. We show that there exists a Reebless co-orientable foliation $mathcal{F}$ in $M_0$, whose leaves may be transverse to $partial M_0$ or tangent to $partial M_0$ at their intersections with $partial M_0$, such that $mathcal{F}$ has a transverse $(pi_1(M_0),mathbb{R})$ structure, and $mathcal{F}$ is analogue to taut foliations (in closed $3$-manifolds) in the following sense: there exists a compact $1$-manifold (i.e. a finite union of properly embedded arcs and/or simple closed curves) transverse to $mathcal{F}$ that intersects every leaf of $mathcal{F}$. We conjecture that $mathcal{F}$ is obtained from removing a $3$-ball foliated with horizontal disks from a taut foliation in $M$.
In this paper, we prove a number of inequalities between the signature and the Betti numbers of a 4-manifold with even intersection form. Furthermore, we introduce a new geometric group invariant and discuss some of its properties.
We classify those compact 3-manifolds with incompressible toral boundary whose fundamental groups are residually free. For example, if such a manifold $M$ is prime and orientable and the fundamental group of $M$ is non-trivial then $M cong Sigmatimes S^1$, where $Sigma$ is a surface.
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