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This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries.
This book describes classic and new results on solvability and unsolvability of equations in explicit form, presenting the author's complete exposition of topological Galois theory, plus basics of the Picard-Vessiot theory and a great deal more.
By Vin de Silva
The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented 2 -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index...
Unlike other analytic techniques, the Homotopy Analysis Method HAM is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the...
Based on a graduate course, this introduction to modern methods of symplectic topology explains the solution of an important problem originating from classical mechanics: the 'Arnold conjecture'. Presents building blocks of Floer homology and more.
By Jean Gallier
This book offers a detailed proof of the classification theorem for compact surfaces. It presents the technical tools needed to deploy the method effectively as well as demonstrates their use in a clearly structured, worked example.
Provides an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. This title covers frictional properties of knots, relations with combinatorics, and knots in dynamical systems. It includes articles Khovanov Homology.
This book offers a foundation for arithmetic topology, a new branch of mathematics focused upon the analogy between knot theory and number theory. The coverage includes background information and theory, along with numerous useful examples and illustrations.