Softcover ISBN:  9780821838457 
Product Code:  CMIP/5 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
Softcover ISBN:  9780821838457 
Product Code:  CMIP/5 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 

Book DetailsClay Mathematics ProceedingsVolume: 5; 2006; 297 ppMSC: Primary 57; 53; 14
Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electroweak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of fourmanifolds was pioneered by the fundamental work of Simon Donaldson in the early 1980s, and was revolutionized by the introduction of the Seiberg–Witten equations in the mid1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's construction of an infinitedimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological invariants for threemanifolds, which fit into a framework for calculating invariants for smooth fourmanifolds. “Heegaard Floer homology”, the recentlydiscovered invariant for three and fourmanifolds, comes from an application of Lagrangian Floer homology to spaces associated to Heegaard diagrams. Although this theory is conjecturally isomorphic to Seiberg–Witten theory, it is more topological and combinatorial in flavor and thus easier to work with in certain contexts. The interaction between gauge theory, lowdimensional topology, and symplectic geometry has led to a number of striking new developments in these fields. The aim of this volume is to introduce graduate students and researchers in other fields to some of these exciting developments, with a special emphasis on the very fruitful interplay between disciplines.
This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material to that presented at the school, and the resulting volume provides a stateoftheart introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth fourmanifold topology, and symplectic fourmanifolds.
Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
ReadershipGraduate students and research mathematicians interested in low dimensional, contact and symplectic topology, and gauge theory.

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Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electroweak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of fourmanifolds was pioneered by the fundamental work of Simon Donaldson in the early 1980s, and was revolutionized by the introduction of the Seiberg–Witten equations in the mid1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's construction of an infinitedimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological invariants for threemanifolds, which fit into a framework for calculating invariants for smooth fourmanifolds. “Heegaard Floer homology”, the recentlydiscovered invariant for three and fourmanifolds, comes from an application of Lagrangian Floer homology to spaces associated to Heegaard diagrams. Although this theory is conjecturally isomorphic to Seiberg–Witten theory, it is more topological and combinatorial in flavor and thus easier to work with in certain contexts. The interaction between gauge theory, lowdimensional topology, and symplectic geometry has led to a number of striking new developments in these fields. The aim of this volume is to introduce graduate students and researchers in other fields to some of these exciting developments, with a special emphasis on the very fruitful interplay between disciplines.
This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material to that presented at the school, and the resulting volume provides a stateoftheart introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth fourmanifold topology, and symplectic fourmanifolds.
Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
Graduate students and research mathematicians interested in low dimensional, contact and symplectic topology, and gauge theory.