Potential theory and geometry on Lie groups / N. Th. Varopoulos.

Format:

Book

Author/Creator:

Varopoulos, N., 1940- author.

Series:

New mathematical monographs ; 38.

New mathematical monographs ; 38

Language:

English

Subjects (All):

Lie groups.

Geometry.

Potential theory (Mathematics).

Physical Description:

1 online resource (xxvii, 596 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Language Note:

English

Summary:

This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further.

Contents:

The classification and the first main theorem

NC-groups

The B-NB classification

NB-Groups

Other classes of locally compact groups

The geometric theory. An introduction

The geometric NC-theorem

Algebra and geometries on C-groups

The end game in the C-theorem

The metric classification

The homotopy and homology classification of connected Lie groups

The polynomial homology for simply connected soluble groups

Cohomology on Lie groups.

Notes:

Title from publisher's bibliographic system (viewed on 29 Oct 2020).

Includes bibliographical references and index.

ISBN:

1-108-76078-3

1-139-56771-3