Foliations and the Geometry of 3-manifolds
by Danny Calegari
Publisher: Oxford University Press 2007
Number of pages: 371
The purpose of this book is to give an exposition of the "pseudo-Anosov" theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms, and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
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by Frank Quinn, Andrew Ranicki
Homology manifolds were developed in the 20th century to give a precise setting for Poincare's ideas on duality. They are investigated using algebraic and geometric methods. This volume is the proceedings of a workshop held in 2003.
by Andrew Ranicki, Norman Levitt, Frank Quinn - Springer
The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.
by Ben Webster - arXiv
We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel...
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In 1970, Sullivan circulated this set of notes introducing localization and completion of topological spaces to homotopy theory, and other important concepts. The notes remain worth reading for the fresh picture they provide for geometric topology.