Surveys in 3-manifold topology -- New developments in Ricci flow with surgery -- Geometric methods in Heegaard theory -- Foliations, contact structures and their interactions in dimension three -- Legendrian contact homology in R3 -- Algorithms in 3-manifold theory -- Toward and after virtual specialization in 3-manifold topology -- Some groups with planar boundaries -- Cannon-Thurston maps in Kleinian groups and geometric group theory -- Volumes of quasifuchsian manifolds.
Summary:
"In the last half-century, tremendous progress has been made in the study of 3-dimensional topology. Many revolutions in 3-manifold topology during this period have come from outside of the field, including Kleinian groups, minimal surfaces, foliations, von Neumann algebras, gauge theory, mathematical physics, 4-manifolds, symplectic topology, contact topology, Riemannian geometry and PDEs, number theory, dynamics, and geometric group theory. The influx of ideas from neighboring fields has made the subject of 3-manifolds (and more generally low-dimensional topology) a very rich subject, creating subfields such as quantum topology. But this also means that there is a tremendous amount of background material for a novitiate in the subject to learn and master"--Publisher.
Series:
Surveys in differential geometry, 1052-9233 ; Volume 25
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.