Modulo 2 counting of Klein-bottle leaves in smooth taut foliations

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2701-2727
Number of pages27
JournalAlgebraic and Geometric Topology
Volume18
Issue number5
DOIs
StatePublished - Aug 28 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • J–holomorphic curves
  • Taut foliations

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