Hokkaido Mathematical Journal

MOCHIZUKI Shinichi, TAMAGAWA Akio,

The algebraic and anabelian geometry of configuration spaces.

Hokkaido Mathematical Journal, 37 (2008) pp.75-131

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Abstract

In this paper, we study the pro-$\Sigma$ fundamental groups of configuration, where $\Sigma$ is either the set of all prime numbers or a set consisting of a single prime number. In particular, we show, via two somewhat distinct approaches, that, in many cases, the "fiber subgroups" of such fundamental groups arising from the various natural projections of a configuration space to lower-dimensional configuration spaces may be characterized group-theoretically.

MSC(Primary)
MSC(Secondary)14H10(MSC2000), 14H30(MSC2000)
Uncontrolled Keywordshyperbolic curve, configuration space, anabelian, ├ętale fundamental group, profinite group, surface group.