東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Twisted isospectrality, homological ...

Cornelissen, Gunther.

FindBook

Google Book

Amazon

博客來

Twisted isospectrality, homological wideness, and isometry = a sample of algebraic methods in isospectrality /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Twisted isospectrality, homological wideness, and isometry/ by Gunther Cornelissen, Norbert Peyerimhoff.
其他題名:	a sample of algebraic methods in isospectrality /
作者:	Cornelissen, Gunther.
其他作者:	Peyerimhoff, Norbert.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xvi, 111 p. :ill., digital ;24 cm.
內容註:	Chapter. 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.
Contained By:	Springer Nature eBook
標題:	Isometrics (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-031-27704-7
ISBN:	9783031277047

Twisted isospectrality, homological wideness, and isometry = a sample of algebraic methods in isospectrality /
Cornelissen, Gunther.

Twisted isospectrality, homological wideness, and isometrya sample of algebraic methods in isospectrality /[electronic resource] :by Gunther Cornelissen, Norbert Peyerimhoff. - Cham :Springer International Publishing :2023. - xvi, 111 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

Chapter. 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.

Open access.

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) 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.

ISBN: 9783031277047

Standard No.: 10.1007/978-3-031-27704-7doiSubjects--Topical Terms:

596358
Isometrics (Mathematics)

LC Class. No.: QA601 / .C67 2023

Dewey Class. No.: 515.723

Twisted isospectrality, homological wideness, and isometry = a sample of algebraic methods in isospectrality /
LDR:03581nmm a2200349 a 4500 001 2373673
003 DE-He213
005 20231230001219.0
006 m d
007 cr nn 008maaau
008 241231s2023 sz s 0 eng d
020 $a 9783031277047 $q (electronic bk.)
020 $a 9783031277030 $q (paper)
024 7 $a 10.1007/978-3-031-27704-7 $2 doi
035 $a 978-3-031-27704-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA601 $b .C67 2023
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515.723 $2 23
090 $a QA601 $b .C814 2023
100 1 $a Cornelissen, Gunther. $3 3721993
245 1 0 $a Twisted isospectrality, homological wideness, and isometry $h [electronic resource] : $b a sample of algebraic methods in isospectrality / $c by Gunther Cornelissen, Norbert Peyerimhoff.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xvi, 111 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8201
505 0 $a Chapter. 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 $a Open access.
520 $a 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) 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 $a Isometrics (Mathematics) $3 596358
650 0 $a Riemannian manifolds. $3 540526
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Manifolds and Cell Complexes. $3 3538507
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Algebraic Topology. $3 891269
650 2 4 $a Differential Geometry. $3 891003
700 1 $a Peyerimhoff, Norbert. $3 3721994
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in mathematics. $3 1566700
856 4 0 $u https://doi.org/10.1007/978-3-031-27704-7
950 $a Mathematics and Statistics (SpringerNature-11649)