000			04740nam a22006255i 4500
001			978-3-031-27704-7
003			DE-He213
005			20240508090327.0
007			cr nn 008mamaa
008			230510s2023 sz | s |||| 0|eng d
020			_a9783031277047 _9978-3-031-27704-7
024	7		_a10.1007/978-3-031-27704-7 _2doi
050		4	_aQA614-614.97
072		7	_aPBK _2bicssc
072		7	_aMAT034000 _2bisacsh
072		7	_aPBK _2thema
082	0	4	_a514.74 _223
100	1		_aCornelissen, Gunther. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aTwisted Isospectrality, Homological Wideness, and Isometry _h[electronic resource] : _bA Sample of Algebraic Methods in Isospectrality / _cby Gunther Cornelissen, Norbert Peyerimhoff.
250			_a1st ed. 2023.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2023.
300			_aXVI, 111 p. 1 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringerBriefs in Mathematics, _x2191-8201
505	0		_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.
506	0		_aOpen Access
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.
650		0	_aGlobal analysis (Mathematics).
650		0	_aManifolds (Mathematics).
650		0	_aNumber theory.
650		0	_aGroup theory.
650		0	_aAlgebraic topology.
650		0	_aGeometry, Differential.
650	1	4	_aGlobal Analysis and Analysis on Manifolds.
650	2	4	_aManifolds and Cell Complexes.
650	2	4	_aNumber Theory.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aAlgebraic Topology.
650	2	4	_aDifferential Geometry.
700	1		_aPeyerimhoff, Norbert. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
710	2		_aSpringerLink (Online service)
773	0		_tSpringer Nature eBook
776	0	8	_iPrinted edition: _z9783031277030
776	0	8	_iPrinted edition: _z9783031277054
830		0	_aSpringerBriefs in Mathematics, _x2191-8201
856	4	0	_uhttps://doi.org/10.1007/978-3-031-27704-7
912			_aZDB-2-SMA
912			_aZDB-2-SXMS
912			_aZDB-2-SOB
999			_c37773 _d37773