Normal Tori in ${♯}_n(S^2\times S^1)$

Abstract

The fundamental group of $M={♯}_n(S^2\times S^1)$ is $F_n$, the free group with $n$ generators. There is a 1-1 correspondence between the equivalence classes of $\mathbb{Z}$-- splittings of $F_n$ and homotopy classes of embedded essential tori in $M$. We define and prove a local notion of minimal intersection of a torus with respect to a maximal sphere system in $M$, which generalizes Hatcher's work \cite{H1} on 2-spheres in the same manifold.

14 pages, 4 figures

References in corpus (3)

• Homology stability for outer automorphism groups of free groups
• Automorphisms of the graph of free splittings
• Algebraic and Geometric intersection numbers for free groups