Abstract
Cobordism of Haken $n$-manifolds is defined by a Haken $(n+1)$-manifold $W$ whose boundary has two components, each of which is a closed Haken $n$-manifold. In addition, the inclusion map of the fundamental group of each boundary component to $\pi_{1}(W)$ is injective. In this paper, we prove that there are $4$-dimensional Haken cobordisms whose boundary consists of any two closed Haken $3$-manifolds. In particular, each closed Haken $3$-manifold is the $\pi_{1}$-injective boundary of some Haken $4$-manifold.
Citation
Bell Foozwell. Hyam Rubinstein. "Four-dimensional Haken cobordism theory." Illinois J. Math. 60 (1) 1 - 17, Spring 2016. https://doi.org/10.1215/ijm/1498032021
Information