Low-Dimensional Solenoidal Manifolds

Explore the fascinating world of low-dimensional solenoidal manifolds in this comprehensive lecture. Delve into a survey of n-dimensional solenoidal manifolds for n=1, 2, and 3, and discover new findings in this field. Gain insights into the nature of solenoidal manifolds as metric spaces locally modeled on the product of a Cantor set and an open n-dimensional disk, understanding their "laminated" or "foliated" structure with n-dimensional leaves. Examine the theorem by A. Clark and S. Hurder, which states that topologically homogeneous, compact solenoidal manifolds are McCord solenoids. Investigate the rich structure of these manifolds as principal Cantor-group bundles over compact manifolds, and learn how they behave like "laminated" versions of compact manifolds, sharing many of their properties. This in-depth talk provides a comprehensive overview of the subject, offering valuable insights for mathematicians and researchers interested in low-dimensional topology and geometric structures.