By Matthias Aschenbrenner, Stefan Friedl, Henry Wilton

The sector of 3-manifold topology has made nice strides ahead considering that 1982 whilst Thurston articulated his influential checklist of questions. fundamental between those is Perelman's evidence of the Geometrization Conjecture, yet different highlights comprise the Tameness Theorem of Agol and Calegari-Gabai, the skin Subgroup Theorem of Kahn-Markovic, the paintings of clever and others on targeted dice complexes, and, eventually, Agol's facts of the digital Haken Conjecture. This ebook summarizes these kind of advancements and offers an exhaustive account of the present cutting-edge of 3-manifold topology, in particular concentrating on the implications for basic teams of 3-manifolds. because the first ebook on 3-manifold topology that includes the fascinating development of the final 20 years, will probably be a useful source for researchers within the box who desire a reference for those advancements. It additionally provides a fast moving advent to this fabric. even supposing a few familiarity with the elemental staff is suggested, little different past wisdom is thought, and the publication is available to graduate scholars. The ebook closes with an in depth checklist of open questions as a way to even be of curiosity to graduate scholars and confirmed researchers. A book of the ecu Mathematical Society (EMS). allotted in the Americas through the yankee Mathematical Society.