001467590 000__ 04820cam\\22006257i\4500
001467590 001__ 1467590
001467590 003__ OCoLC
001467590 005__ 20230707003330.0
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001467590 008__ 230518s2023\\\\sz\a\\\\ob\\\\001\0\eng\d
001467590 019__ $$a1381176573
001467590 020__ $$a9783031277047$$q(electronic bk.)
001467590 020__ $$a303127704X$$q(electronic bk.)
001467590 020__ $$z9783031277030
001467590 020__ $$z3031277031
001467590 0247_ $$a10.1007/978-3-031-27704-7$$2doi
001467590 035__ $$aSP(OCoLC)1379266708
001467590 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDX
001467590 049__ $$aISEA
001467590 050_4 $$aQA601
001467590 08204 $$a515/.723$$223/eng/20230518
001467590 1001_ $$aCornelissen, Gunther,$$d1971-$$eauthor.
001467590 24510 $$aTwisted isospectrality, homological wideness, and isometry :$$ba sample of algebraic methods in isospectrality /$$cGunther Cornelissen, Norbert Peyerimhoff.
001467590 264_1 $$aCham :$$bSpringer,$$c2023.
001467590 300__ $$a1 online resource (xvi, 111 pages) :$$billustrations.
001467590 336__ $$atext$$btxt$$2rdacontent
001467590 337__ $$acomputer$$bc$$2rdamedia
001467590 338__ $$aonline resource$$bcr$$2rdacarrier
001467590 4901_ $$aSpringerBriefs in mathematics,$$x2191-8201
001467590 504__ $$aIncludes bibliographical references and index.
001467590 5050_ $$aChapter. 1. Introduction -- Part I: Leitfaden -- Chapter. 2. Manifold and orbifold constructions -- Chapter. 3. Spectra, group representations and twisted Laplacians -- Chapter. 4. Detecting representation isomorphism through twisted spectra -- Chapter. 5. Representations with a unique monomial structure -- Chapter. 6. Construction of suitable covers and proof of the main theorem -- Chapter. 7. Geometric construction of the covering manifold -- Chapter. 8. Homological wideness -- Chapter. 9. Examples of homologically wide actions -- Chapter. 10. Homological wideness, "class field theory" for covers, and a number theoretical analogue -- Chapter. 11. Examples concerning the main result -- Chapter. 12. Length spectrum -- References -- Index.
001467590 5060_ $$aOpen access.$$5GW5XE
001467590 520__ $$aThe question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings). The methods outlined in the book fit into the tradition of the famous work of Sunada on the construction of isospectral, non-isometric manifolds, and thus do not focus on analytic techniques, but rather on algebraic methods: in particular, the analogy with constructions in number theory, methods from representation theory, and from algebraic topology. The main goal of the book is to present the construction of finitely many "twisted" Laplace operators whose spectrum determines covering equivalence of two Riemannian manifolds. The book has a leisure pace and presents details and examples that are hard to find in the literature, concerning: fiber products of manifolds and orbifolds, the distinction between the spectrum and the spectral zeta function for general operators, strong isospectrality, twisted Laplacians, the action of isometry groups on homology groups, monomial structures on group representations, geometric and group-theoretical realisation of coverings with wreath products as covering groups, and "class field theory" for manifolds. The book contains a wealth of worked examples and open problems. After perusing the book, the reader will have a comfortable working knowledge of the algebraic approach to isospectrality. This is an open access book.
001467590 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed May 18, 2023).
001467590 650_0 $$aIsometrics (Mathematics)
001467590 650_0 $$aRiemannian manifolds.
001467590 655_0 $$aElectronic books.
001467590 7001_ $$aPeyerimhoff, Norbert,$$d1964-$$eauthor.
001467590 77608 $$iPrint version: $$z3031277031$$z9783031277030$$w(OCoLC)1369513602
001467590 830_0 $$aSpringerBriefs in mathematics,$$x2191-8201
001467590 852__ $$bebk
001467590 85640 $$3Springer Nature$$uhttps://link.springer.com/10.1007/978-3-031-27704-7$$zOnline Access$$91397441.2
001467590 909CO $$ooai:library.usi.edu:1467590$$pGLOBAL_SET
001467590 980__ $$aBIB
001467590 980__ $$aEBOOK
001467590 982__ $$aEbook
001467590 983__ $$aOnline
001467590 994__ $$a92$$bISE