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Twisted Isospectrality, Homological Wideness, and Isometry A Sample of Algebraic Methods in Isospectrality /

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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 on...

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Bibliographic Details
Main Authors: Cornelissen, Gunther (Author), Peyerimhoff, Norbert (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2023.
Edition:1st ed. 2023.
Series:SpringerBriefs in Mathematics,
Subjects:
Global analysis (Mathematics).
Manifolds (Mathematics).
Number theory.
Group theory.
Algebraic topology.
Geometry, Differential.
Global Analysis and Analysis on Manifolds.
Manifolds and Cell Complexes.
Number Theory.
Group Theory and Generalizations.
Algebraic Topology.
Differential Geometry.
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Table of Contents:
  • 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.

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