viii CONTENTS
Incompressibility of the boundary tori 139
Structure of Mt,thin(w) 139
Lecture 31 141
The relative version of the Geometrization Conjecture 141
Proof that the theorem implies Geometrization Conjecture 142
Study of Mt,thin(w) 142
Lecture 32 145
The structure of sufficiently volume collapsed 3-manifolds 145
Gromov-Hausdorff limits 145
Alexandrov spaces 145
Structure of the ρ−1(xn)B(xn,ρ(xn)) when the limit has dimension 1 147
Structure of the
ρ−1(xn)B(xn,ρ(xn))
when the limit has dimension 2 147
The global structure 148
Bibliography 149
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