{"product_id":"twisted-isospectrality-homological-wideness-and-isometry-a-sample-of-algebraic-methods-in-isospectrality-9783031277030","title":"Twisted Isospectrality, Homological Wideness, and Isometry: A Sample of Algebraic Methods in Isospectrality","description":"The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings).\u003cbr\u003eThe methods outlined in the book fit into the tradition of the famous work of Sunada on the construction of isospectral, non-isometric manifolds, and thus do \u003ci\u003enot\u003c\/i\u003e focus on analytic techniques, but rather on algebraic methods: in particular, the analogy with constructions in number theory, methods from representation theory, and from algebraic topology.\u003cbr\u003e\u003cp\u003eThe main goal of the book is to present the construction of finitely many \"twisted\" Laplace operators whose spectrum determines covering equivalence of two Riemannian manifolds.\u003c\/p\u003e\u003cp\u003eThe book has a leisure pace and presents details and examples that are hard to find in the literature, concerning: fiber products of manifolds and orbifolds, the distinction between the spectrum and the spectral zeta function for general operators, strong isospectrality, twisted Laplacians, the action of isometry groups on homology groups, monomial structures on group representations, geometric and group-theoretical realisation of coverings with wreath products as covering groups, and \"class field theory\" for manifolds. The book contains a wealth of worked examples and open problems. After perusing the book, the reader will have a comfortable working knowledge of the algebraic approach to isospectrality. \u003c\/p\u003e\u003cp\u003eThis is an open access book.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Gunther Cornelissen, Norbert Peyerimhoff\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 05\/11\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 111\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.42lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.27d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9783031277030\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eGunther Cornelissen\u003c\/b\u003e holds the chair of geometry and number theory at Utrecht University. He earned his PhD from Ghent University in 1997 and has held visiting positions at institutions such as the Max Planck Institute for Mathematics in Bonn, Leuven University, California Institute of Technology and the University of Warwick. His research focuses on Arithmetic Geometry, particularly in positive characteristic, and also branches off into areas such as Spectral Geometry, Undecidability, Algebraic Dynamics and Graph Algorithms.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eNorbert Peyerimhoff\u003c\/b\u003e received his PhD in Mathematics in 1993 from the University of Augsburg. He held postdoctoral positions at the City University of New York, was an Assistant at the University of Basel and at the Ruhr University Bochum, before moving to Durham University (United Kingdom) in 2004. He has been a Professor of Geometry at Durham University since 2013, and his research interests include Differential Geometry, Discrete Geometry, Lie groups, Dynamical Systems, Spectral Theory and X-Ray Crystallography.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":41094739787891,"sku":"9.78303E+12","price":64.51,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/products\/img_0c7ad6f0-818d-44a0-8a98-d17af3779896.jpg?v=1699971552","url":"https:\/\/bookstorenmore.com\/products\/twisted-isospectrality-homological-wideness-and-isometry-a-sample-of-algebraic-methods-in-isospectrality-9783031277030","provider":"Bookstore N More","version":"1.0","type":"link"}