Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2022; 59(4): 699-715

Published online July 1, 2022 https://doi.org/10.4134/JKMS.j210535

Copyright © The Korean Mathematical Society.

Foliations from left orders

Hyungryul Baik, Sebastian Hensel, Chenxi Wu

KAIST; University of Munich; University of Wisconsin – Madison

Abstract

We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension $2$, and exhibit connections to various problems in dimension $3$.

Keywords: Left-invariant order, orderable group, geodesic lamination, foliation

MSC numbers: Primary 57R30, 06F15

Supported by: Hyungryul Baik was partially supported by Samsung Science \& Technology Foundation grant No. SSTF-BA1702-01, and Sebastian Hensel was partially supported by the DFG SPP 2026 ``Geometry at Infinity".