Solenoidal Manifolds

Journal of Singularities
volume 9 (2014), 203-205

Received 31 December 2012. Received in revised form 17 May 2013.

DOI: 10.5427/jsing.2014.9o

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Abstract:

It is shown that every oriented solenoidal manifold of dimension one is the boundary of a compact oriented solenoidal 2-manifold. For compact solenoidal surfaces one can develop a theory of complex structures parallel to the theory for Riemann surfaces. In particular, there exists a corresponding Teichmüller space. The Teichmüller space of the solenoidal surface obtained by taking the inverse limit of all finite pointed covers of a compact surface of genus greater than one is a separable Banach manifold version of the universal Teichmüller space of the upper half plane which is not separable. The commensurability automorphism group of the fundamental group of the surface acts minimally on this solenoidal version of the universal Teichmüller space.

Author(s) information:

Dennis Sullivan