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.
Hyungryul Baik, Sebastian Hensel, Chenxi Wu
KAIST; University of Munich; University of Wisconsin – Madison
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".
2008; 45(3): 859-870
2008; 45(4): 965-976
2009; 46(5): 1087-1103
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