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

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, Peyerimhoff, Norbert (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2023, 2023
Edition:1st ed. 2023
Series:SpringerBriefs in Mathematics
Subjects:
Group Theory And Generalizations
Number Theory
Geometry, Differential
Algebraic Topology
Group Theory
Manifolds And Cell Complexes
Manifolds (mathematics)
Differential Geometry
Global Analysis (mathematics)
Global Analysis And Analysis On Manifolds
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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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