Lifts of simple curves in finite regular coverings of closed surfaces

2015/08/19 by Ingrid Irmer, Irmer, Ingrid
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1508.04815

Final rewrite

arxiv created 2018/05/22 · arxiv updated 2018/05/23

Abstract

Suppose S is a closed orientable surface and S is a finite sheeted regular cover of S. The following question was posed by Julién Marché in Mathoverflow: Do the lifts of simple curves from S generate H₁(S,ℤ)? A family of examples is given for which the answer is "no".

Related

• Simple lift of non-simple closed curves
• Characterizing covers via simple closed curves
• Simple closed curves in stable covers of surfaces
• Generating the homology of covers of surfaces
• Finding simple curves in surface covers is undecidable