Toward the classification of cohomology-free vector fields

2007/06/27 by Alejandro Kocsard, Kocsard, Alejandro
Mathematics · #37C15 #37C55 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.DS #math.GT #msc:37C15 #msc:37C55

paper · pdf · doi:10.48550/arxiv.0706.4053

70 pages, PhD thesis (IMPA, May 2007). Corrected typos

arxiv created 2007/07/11 · arxiv updated 2009/12/01

Abstract

In 1984, Anatole Katok conjectured that the only closed orientable manifolds that support cohomology-free vector fields are tori and these vector fields are smoothly conjugated to Diophantine (constant) ones. In this work we present a proof of Katok conjecture for 3-manifolds.

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