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We introduce two new tools for studying CAT (0) spaces: curtains, versions of cubical
hyperplanes; and the curtain model, a counterpart of the curve graph. These tools shed new …

We give another proof of the result of Masur and Minsky that the complex of curves
associated to a compact orientable surface is hyperbolic. Our proof is more combinatorial in …

We study the large scale geometry of mapping class groups ℳ CG (S), using hyperbolicity
properties of curve complexes. We show that any self quasi-isometry of ℳ CG (S)(outside a …

We present a view of the current understanding of the geometry of Weil-Petersson (WP)
geodesics on the completion of the Teichm\" uller space. We sketch a collection of results by …

" This book is the companion to the CBMS lectures of Scott Wolpert at Central Connecticut
State University. The lectures span across areas of research progress on deformations of …

Throughout, S is an orientable surface whose Euler characteristic χ (S) is negative, while g,
b denotes a surface of genus g with b boundary components. Also, Mod (S) means the …

It is a classical result that pure mapping class groups of connected, orientable surfaces of
finite type and genus at least 3 are perfect. In stark contrast, we construct nontrivial …

We show that any isomorphism between mapping class groups of orientable infinite-type
surfaces is induced by a homeomorphism between the surfaces. Our argument additionally …

The author obtains some classification result for the mapping class groups of compact
orientable surfaces in terms of measure equivalence. In particular, the mapping class groups …