Overview

This text provides an overview of some of the most active topics in the theory of transformation groups over the latter part of the 20th century and stresses advances obtained since around 1990. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semi-algebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into 15 articles and should be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.

Full Product Details

Author:   Anthony Bak ,  Masaharu Morimoto ,  Fumihiro Ushitaki
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2002 ed.
Volume:   7
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   1.220kg
ISBN:  

9781402007835

ISBN 10:   1402007833
Pages:   252
Publication Date:   31 July 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Hilbert’s fifth problem and proper actions of Lie groups.- 2. Equivariant algebraic vector bundles over representations — a survey.- 3. G-manifolds and G-vector bundles in algebraic, semialgebraic, and definable categories.- 4. Geometry of Finite Topological spaces and equivariant finite topological spaces.- 5. On the theory of homotopy representations. A survey.- 6. Manifolds as fixed point sets of smooth compact Lie group actions.- 7. Surgery and homotopy theory in study of the transformation groups.- 8. Kervaire’s obstructions of free actions of finite cyclic groups on homotopy spheres.- 9. The Burnside ring revisited.- 10. Multiplicative stabilization and transformation groups.- 11. Symmetries on manifolds, deformations and rational homotopy: a survey.- 12. Rigidity of codimension one locally free actions of solvable Lie groups.- 13. Smooth actions of non-compact semi-simple Lie groups.- 14. Hamiltonian group actions ana equivariant indices.- 15. Controlled methods in equivariant topology, a survey.

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