Dedication

pp v-vi

Contents

pp vii-xxiv

Preface

pp xxv-xxviii

1 - Chapter

pp 1-20

Part I - Analytic and Algebraic Classification

pp 21-22

2 - The Classification and the First Main Theorem

pp 23-64

3 - NC-Groups

pp 65-97

4 - The B–NB Classification

pp 98-122

5 - NB-Groups

pp 123-167

6 - Other Classes of Locally Compact Groups

pp 168-185

Appendix A - Semisimple Groups and the Iwasawa Decomposition

pp 186-196

Appendix B - The Characterisation of NB-Algebras

pp 197-206

Appendix C - The Structure of NB-Groups

pp 207-209

Appendix D - Invariant Differential Operators and Their Diffusion Kernels

pp 210-215

Appendix E - Additional Results. Alternative Proofs and Prospects

pp 216-220

Part II - Geometric Theory

pp 221-222

7 - Geometric Theory. An Introduction

pp 223-238

8 - The Geometric NC-Theorem

pp 239-266

9 - Algebra and Geometry on C-Groups

pp 267-319

10 - The Endgame in the C-Theorem

pp 320-348

11 - The Metric Classification

pp 349-372

Appendix F - Retracts on General NB-Groups (Not Necessarily Simply Connected)

pp 373-386

Part III - Homology Theory

pp 387-388

12 - The Homotopy and Homology Classification of Connected Lie Groups

pp 389-459

13 - The Polynomial Homology for Simply Connected Soluble Groups

pp 460-518

14 - Cohomology on Lie Groups

pp 519-561

Appendix G - Discrete Groups

pp 562-581

Epilogue

pp 582-584

References

pp 585-588