| Foreword | p. vii |
| Dehn Functions and Non-Positive Curvature | p. 1 |
| Preface | p. 3 |
| The Isoperimetric Spectrum | p. 5 |
| First order Dehn functions and the isoperimetric spectrum | p. 5 |
| Definitions and history | p. 5 |
| Perron-Frobenius eigenvalues and snowflake groups | p. 7 |
| Topological background | p. 9 |
| Graphs of spaces and graphs of groups | p. 10 |
| The torus construction and vertex groups | p. 11 |
| Snowflake groups | p. 15 |
| Snowflake groups and the lower bounds | p. 16 |
| Upper bounds | p. 22 |
| Questions and further explorations | p. 25 |
| Dehn Functions of Subgroups of CAT(0) Groups | p. 29 |
| CAT(0) spaces and CAT(0) groups | p. 31 |
| Definitions and properties | p. 31 |
| M[kappa]-complexes, the link condition | p. 33 |
| Piecewise Euclidean cubical complexes | p. 35 |
| Morse theory I: recognizing free-by-cyclic groups | p. 38 |
| Morse functions and ascending/descending links | p. 38 |
| Morse function criterion for free-by-cyclic groups | p. 42 |
| Groups of type (F[subscript n] [Characters not reproducible] Z) x F[subscript 2] | p. 45 |
| LOG groups and LOT groups | p. 45 |
| Polynomially distorted subgroups | p. 46 |
| Examples: The double construction and the polynomial Dehn function | p. 48 |
| Morse theory II: topology of kernel subgroups | p. 49 |
| A non-finitely generated example: Ker(F[subscript 2 right arrow] Z) | p. 51 |
| A non-finitely presented example: Ker(F[subscript 2] x F[subscript 2 right arrow] Z) | p. 53 |
| A non-F[subscript 3] example: Ker(F[subscript 2] x F[subscript 2] x F[subscript 2 right arrow] Z) | p. 56 |
| Branched cover example | p. 57 |
| Right-angled Artin group examples | p. 57 |
| Right-angled Artin groups, cubical complexes and Morse theory | p. 58 |
| The polynomial Dehn function examples | p. 60 |
| A hyperbolic example | p. 64 |
| Branched covers of complexes | p. 65 |
| Branched covers and hyperbolicity in low dimensions | p. 66 |
| Branched covers in higher dimensions | p. 70 |
| The main theorem and the topological version | p. 71 |
| The main theorem: sketch | p. 72 |
| Bibliography | p. 77 |
| Filling Functions | p. 81 |
| Notation | p. 83 |
| Introduction | p. 85 |
| Filling Functions | p. 89 |
| Van Kampen diagrams | p. 89 |
| Filling functions via van Kampen diagrams | p. 91 |
| Example: combable groups | p. 94 |
| Filling functions interpreted algebraically | p. 99 |
| Filling functions interpreted computationally | p. 100 |
| Filling functions for Riemannian manifolds | p. 105 |
| Quasi-isometry invariance | p. 106 |
| Relationships Between Filling Functions | p. 109 |
| The Double Exponential Theorem | p. 110 |
| Filling length and duality of spanning trees in planar graphs | p. 115 |
| Extrinsic diameter versus intrinsic diameter | p. 119 |
| Free filling length | p. 119 |
| Example: Nilpotent Groups | p. 123 |
| The Dehn and filling length functions | p. 123 |
| Open questions | p. 126 |
| Asymptotic Cones | p. 129 |
| The definition | p. 129 |
| Hyperbolic groups | p. 132 |
| Groups with simply connected asymptotic cones | p. 137 |
| Higher dimensions | p. 141 |
| Bibliography | p. 145 |
| Diagrams and Groups | p. 153 |
| Introduction | p. 155 |
| Dehn's Problems and Cayley Graphs | p. 157 |
| Van Kampen Diagrams and Pictures | p. 163 |
| Small Cancellation Conditions | p. 179 |
| Isoperimetric Inequalities and Quasi-Isometries | p. 187 |
| Free Nilpotent Groups | p. 197 |
| Hyperbolic-by-free groups | p. 201 |
| Bibliography | p. 205 |
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