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11 The Bieri–Neumann–Strebel Invariant
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Chapters in this book
- Frontmatter i
- Contents v
- Preface xi
- 1 Introduction 1
- 2 Riemann Surfaces and Orbifolds 19
- 3 The Fibration Problem: From Infinite to Finite Covers 35
- 4 The Theorem of Castelnuovo–de Franchis and Its Variants 40
- 5 Many Fibration Criteria 53
- 6 Kähler Groups and Trees 67
- 7 Covering Spaces of Compact Kähler Manifolds and Ends 90
- 8 Representations into PSL2(C) 106
- 9 Harmonic Maps to Locally Symmetric Spaces 122
- 10 Lattices and Groups of Hodge Type 162
- 11 The Bieri–Neumann–Strebel Invariant 185
- 12 The Green–Lazarsfeld Set 212
- 13 Actions on Real Trees 239
-
APPENDICES
- A Ends of Spaces and Groups 251
- B Groups Acting on Trees 265
- C Affine Actions on Hilbert Spaces 283
- D Harmonic Functions of Finite Energy 305
- E Potential Theory 317
- F Nakai’s Theorem 330
- G Diederich and Mazzilli’s Theorem 341
- H Harmonic Maps and Nonpositive Hermitian Curvature 350
- Bibliography 357
- Index 381
Chapters in this book
- Frontmatter i
- Contents v
- Preface xi
- 1 Introduction 1
- 2 Riemann Surfaces and Orbifolds 19
- 3 The Fibration Problem: From Infinite to Finite Covers 35
- 4 The Theorem of Castelnuovo–de Franchis and Its Variants 40
- 5 Many Fibration Criteria 53
- 6 Kähler Groups and Trees 67
- 7 Covering Spaces of Compact Kähler Manifolds and Ends 90
- 8 Representations into PSL2(C) 106
- 9 Harmonic Maps to Locally Symmetric Spaces 122
- 10 Lattices and Groups of Hodge Type 162
- 11 The Bieri–Neumann–Strebel Invariant 185
- 12 The Green–Lazarsfeld Set 212
- 13 Actions on Real Trees 239
-
APPENDICES
- A Ends of Spaces and Groups 251
- B Groups Acting on Trees 265
- C Affine Actions on Hilbert Spaces 283
- D Harmonic Functions of Finite Energy 305
- E Potential Theory 317
- F Nakai’s Theorem 330
- G Diederich and Mazzilli’s Theorem 341
- H Harmonic Maps and Nonpositive Hermitian Curvature 350
- Bibliography 357
- Index 381