GEOMETRY OF SPHERICAL SPACE FORM GROUPS, THE (SECOND EDITION) (Pure Mathematics, 28)

Peter B Gilkey

ISBN 10: 9813220783 / ISBN 13: 9789813220782

Published by World Scientific Publishing Company, 2018

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Bibliographic Details

• Title: GEOMETRY OF SPHERICAL SPACE FORM GROUPS, THE (SECOND EDITION) (Pure Mathematics, 28)
• Publisher: World Scientific Publishing Company
• Publication Date: 2018
• Language: English
• ISBN 10: 9813220783
• ISBN 13: 9789813220782
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: New

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Synopsis

This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.

This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.