Alberto Verjovsky (Instituto de Matemáticas-UNAM, Mexico)

Compact 3-dimensional geometric solenoidal manifolds

Abstract: We present several results about solenoidal manifolds motivated by results by Dennis Sullivan in [1] with commentaries developed in [2] and on a join project with Dennis Sullivan [3]. Solenoidal manifolds of dimension n are topological spaces which are locally homeomorphic to the product of a Cantor set with an open subset of $R^n$. Geometric 3-dimensional solenoidal manifolds are the analog of geometric 3-manifolds in the sense of Thurston. We will give some results related to 3-dimensional geometric solenoidal manifolds.

[1] D. Sullivan, Solenoidal manifolds, J. Singul. 9 (2014), 203–205.
[2] A. Verjovsky, Commentaries on the paper “Solenoidal manifolds” by Dennis Sullivan. J. Singul. 9 (2014), 245–251.
[3] D. Sullivan, A. Verjovsky, Compact 3-dimensional geometric solenoidal manifolds. In preparation.