Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Ii Av Yuichiro Hoshi, Shinichi Mochizuki

<div>The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of <i>configuration spaces</i> associated to <i>hyperbolic curves</i> over algebraically closed fields of characteristic zero.</div><div><br></div><div>The starting point of the theory of the present monograph is a <i>combinatorial anabelian</i> result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give <i>purely group-theoretic characterizations</i> of the <i>cuspidal inertia subgroups</i> of one-dimensional subquotients of the profinite fundamental group of a configuration space.</div><div><br></div><div>We then turn to the study of <i>tripod synchronization</i>, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve induces