Open Access
Spring 2016 Four-dimensional Haken cobordism theory
Bell Foozwell, Hyam Rubinstein
Illinois J. Math. 60(1): 1-17 (Spring 2016). DOI: 10.1215/ijm/1498032021

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

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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

Received: 14 April 2015; Revised: 18 August 2015; Published: Spring 2016
First available in Project Euclid: 21 June 2017

zbMATH: 1375.57027
MathSciNet: MR3665167
Digital Object Identifier: 10.1215/ijm/1498032021

Subjects:
Primary: 55N22 , 57N10 , 57N13 , 57Q20

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

Vol.60 • No. 1 • Spring 2016
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