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4 produkter
4 produkter
Del 151 - Cambridge Tracts in Mathematics
Frobenius Manifolds and Moduli Spaces for Singularities
Inbunden, Engelska, 2002
1 521 kr
Skickas inom 7-10 vardagar
The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will find here a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.
Triangular Bases of Unimodular Bilinear Lattices and Induced Structures
Automorphism Groups, Vanishing Cycles, Monodromy Groups, Braid Group Actions and Moduli Spaces
Häftad, Engelska, 2026
1 199 kr
Kommande
This monograph presents a structured and conceptually unified study of upper triangular integer matrices and the rich family of structures they induce. Central objects include unimodular bilinear lattices, vanishing cycles, monodromy groups, braid group actions, and associated moduli spaces. These constructions naturally provide a common framework linking algebraic geometry, representation theory, singularity theory, and the theory of irregular meromorphic connections. To a given matrix is associated a ℤ-lattice with a unimodular bilinear form (the Seifert form) and a triangular basis. This leads to even and odd intersection forms, reflections and transvections, monodromy groups, and corresponding vanishing cycles. Braid group actions generate orbits of distinguished bases and matrices, which in turn give rise to complex manifolds obtained by gluing Stokes regions. General tools and results are developed throughout, with a systematic analysis of the cases of rank 2 and 3. Already in rank 3 a wide range of phenomena appears, illustrating the broader landscape. Classical situations related to Coxeter groups, generalized Cartan lattices, exceptional sequences, and isolated hypersurface singularities arise as special cases but represent only a small part of the theory. The book is intended for researchers and students working with integral upper triangular matrices and their induced structures.
Del 2198 - Lecture Notes in Mathematics
Painlevé III: A Case Study in the Geometry of Meromorphic Connections
Häftad, Engelska, 2017
412 kr
Skickas inom 10-15 vardagar
The purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painlevé equations, and it offers new results on a particular Painlevé III equation of type PIII (D6), called PIII (0, 0, 4, −4), describing its relation to isomonodromic families of vector bundles on P1 with meromorphic connections. This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics. It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections. Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed. These provide examples of variations of TERP structures, which are related to tt∗ geometry and harmonic bundles. As an application, a new global picture o0 is given.
Del 36 - Aspects of Mathematics
Frobenius Manifolds
Quantum Cohomology and Singularities
Häftad, Engelska, 2012
1 179 kr
Skickas inom 10-15 vardagar
Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in Bonn, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and presents the state of the art in the subject.