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#### The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44)

Princeton University Press 2014; US$ 55.00The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful... more...

#### Lectures on the Topology of 3-Manifolds

De Gruyter 2011; US$ 979.00This textbook ?now in its second revised and extended edition ?introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology,... more...

#### Grassmannians of Classical Buildings

World Scientific Publishing Company 2010; US$ 103.00Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It gives a modern interpretation of some classical results... more...

#### Relative Index Theory, Determinants and Torsion for Open Manifolds

World Scientific Publishing Company 2009; US$ 121.00For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators... more...

#### Monopoles and Three-Manifolds

Cambridge University Press 2007; US$ 61.00A comprehensive treatment of Floer homology, based on the Seiberg?Witten equations, first published in 2007. more...

#### Outer Circles

Cambridge University Press 2007; US$ 79.00Excellent introductory text on the contemporary theory of hyperbolic 3-manifolds. more...

#### Topological Invariants of Stratified Spaces

Springer 2007; US$ 139.00Covers the restoration of Poincare duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. This book also includes proofs of decomposition theorems for self-dual sheaves, as well as an explanation of methods for computing twisted characteristic classes. more...

#### Infinite Dimensional Groups and Manifolds

De Gruyter 2004; US$ 84.00The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern-Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large... more...

#### The Reidemeister Torsion of 3-Manifolds

De Gruyter 2003; US$ 182.00This is a state-of-the-art introduction to the work of Franz Reidemeister, Meng Taubes, Turaev, and the author on the concept of torsion and its generalizations. Torsion is the oldest topological (but not with respect to homotopy) invariant that in its almost eight decades of existence has been at the center of many important and surprising discoveries.... more...

#### The Grothendieck Theory of Dessins d'Enfants

Cambridge University Press 1994; US$ 104.00The various articles here unite all of the basics of the study of dessins d'enfants as well as the most recent advances. more...