We prove a modulo 2 invariance for the number of Klein-bottle leaves in taut foliations. Given two smooth cooriented taut foliations, assume that every Klein-bottle leaf has nontrivial linear holonomy, and assume that the two foliations can be smoothly deformed to each other through taut foliations. We prove that the numbers of Kleinbottle leaves in these two foliations must have the same parity.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- J–holomorphic curves
- Taut foliations