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Aspects of Mathematics Ser.: Deformation Spaces : Perspectives on Algebro-Geometric Moduli by Thomas Tradler, Hossein Abbaspour and Matilde Marcolli (2014, Trade Paperback)
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About this product
Product Identifiers
PublisherVieweg Verlag, Friedr, & Sohn Verlagsgesellschaft Mbh
ISBN-103834826693
ISBN-139783834826695
eBay Product ID (ePID)14038832455
Product Key Features
Number of PagesVII, 173 Pages
Publication NameDeformation Spaces : Perspectives on Algebro-Geometric Moduli
LanguageEnglish
Publication Year2014
SubjectGeometry / General, Algebra / General, Topology, Geometry / Algebraic
TypeTextbook
Subject AreaMathematics
AuthorThomas Tradler, Hossein Abbaspour, Matilde Marcolli
SeriesAspects of Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight16 Oz
Item Length9.4 in
Item Width6.6 in
Additional Product Features
Intended AudienceScholarly & Professional
Series Volume Number40
Number of Volumes1 vol.
IllustratedYes
Table Of ContentOn the Hochschild and Harrison (co)homology of C ?-algebras and applications to string topology.- What is the Jacobian of a Riemann Surface with Boundary'.- Pure weight perfect Modules on divisorial schemes.- Higher localized analytic indices and strict deformation quantization.- An algebraic proof of Bogomolov-Tian-Todorov theorem.- Quantizing deformation theory.- L ?-interpretation of a classification of deformations of Poisson structures in dimension three.
SynopsisOn the Hochschild and Harrison (co)homology of C ?-algebras and applications to string topology.- What is the Jacobian of a Riemann Surface with Boundary?.- Pure weight perfect Modules on divisorial schemes.- Higher localized analytic indices and strict deformation quantization.- An algebraic proof of Bogomolov-Tian-Todorov theorem.- Quantizing deformation theory.- L ?-interpretation of a classification of deformations of Poisson structures in dimension three., InrecentyearstheHochschildandcycliccomplexandtheiralgebraicstructures have been intensively studied from di'erent perspectives. Some of these algebraic gadgetshavebeenaroundsincetheearlyworkofGerstenhaberonthedeformations of associative algebras, while others, such as cyclic homology, were introduced by Connes in the early development of noncommutative geometry. More recent dev- opments from this perspective include the theory of Hopf cyclic (co)-homology of Hopf algebra. Various algebraic structures of Hochschild and Cyclic (co)-homology, such as Batalin-Vilkoviskyand Gerstenhaber algebras, received a topologicalreincarnation by the works of Chas and Sullivan and other authors on free loop space. These compelling ideas, such as an action of the moduli space of surfaces possibly with various compacti'cations, have been considered in several di'erent settings. The algebraic analogue of these constructions on Hochschild and cyclic complexes (of Frobenius algebras) are usually known under the name of Deligne conjecture. This theory develops parallel to symplectic ?eld theory and Gromov-Witten invariants. As an algebraic theory, this corresponds to a deformation problem over PROPs or properads as opposed to operads, which naturally include genus, or in physics terminology, the correct "h-bar" terms. The editors had organized two workshops in July 2007 and August 2008 at the Max-Planck-Institut fur ¨ Mathematik in Bonn with a generous support from the Hausdor? Center. Participants of these workshops were mainly algebraic topo- gist, noncommutative geometers, and specialists in deformations theory. The aim oftheseworkshopswastobringtogetherthemathematicianswhoworkondefor- tions of algebraic and geometric structures and Hochschild and cyclic complexes. As it is clear from the volume, the subject of these activities was in'uenced by physics and the new perspectives that it o'ers., The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.
LC Classification NumberQA564-609
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