Overview

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. 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, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will 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
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 2002
Volume:   7
Dimensions:   Width: 16.00cm , Height: 1.40cm , Length: 24.00cm
Weight:   0.436kg
ISBN:  

9789401064910

ISBN 10:   9401064911
Pages:   252
Publication Date:   26 September 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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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