L-spaces, taut foliations, and graph manifolds. (23rd March 2020)

• Record Type: Journal Article
• Authors: Hanselman, Jonathan; Rasmussen, Jacob; Rasmussen, Sarah Dean; Watson, Liam
• Is Part Of: Compositio mathematica. Volume 156:Number 3(2020)
• Page Start: 604
• Page End: 612
• Publication Date: 2020-03-23
• Subjects: 57M27; graph manifold, -- L-space, -- taut foliation, -- Heegaard Floer; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X19007814
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : If $Y$ is a closed orientable graph manifold, we show that $Y$ admits a coorientable taut foliation if and only if $Y$ is not an L-space. Combined with previous work of Boyer and Clay, this implies that $Y$ is an L-space if and only if $\unicode[STIX]{x1D70B}_{1}(Y)$ is not left-orderable.