TY - BOOK ID - 14296007 TI - The geometry of infinite-dimensional groups AU - Khesin, Boris A. AU - Wendt, Robert. PY - 2009 VL - 51 SN - 3540772626 3540852050 3540772634 9783540852056 9783540772620 PB - Berlin : Springer, DB - UniCat KW - Infinite dimensional Lie algebras. KW - Lie groups. KW - Algebra KW - Calculus KW - Mathematics KW - Physical Sciences & Mathematics KW - Groups, Lie KW - Lie groups KW - Grupos de KW - MATEMATICAS;LIBROS ELECTRONICOS KW - Mathematics. KW - Algebraic geometry. KW - Group theory. KW - Topological groups. KW - Global analysis (Mathematics). KW - Manifolds (Mathematics). KW - Geometry. KW - Physics. KW - Topological Groups, Lie Groups. KW - Group Theory and Generalizations. KW - Mathematical Methods in Physics. KW - Global Analysis and Analysis on Manifolds. KW - Algebraic Geometry. KW - Lie algebras KW - Symmetric spaces KW - Topological groups KW - Topological Groups. KW - Mathematical physics. KW - Global analysis. KW - Geometry, algebraic. KW - Algebraic geometry KW - Geometry KW - Physical mathematics KW - Physics KW - Euclid's Elements KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Groups, Topological KW - Continuous groups KW - Geometry, Differential KW - Topology KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14296007 AB - This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. While infinite-dimensional groups often exhibit very peculiar features, this book describes unifying geometric ideas of the theory and gives numerous illustrations and examples, ranging from the classification of the Virasoro coadjoint orbits to knot theory, from optimal mass transport to moduli spaces of flat connections on surfaces. The text includes many exercises and open questions, and it is accessible to both students and researchers in Lie theory, geometry, and Hamiltonian systems. ER -