A general Seifert-Van Kampen theorem for algebraic fundamental groups

Abstract

A Seifert-Van Kampen theorem describes the fundamental group of a space in terms of the fundamental groups of the constituents of a covering and the configuration of connected components of the covering. Here we provide the combinatorial part of such a theorem for the most general sort of coverings. Thus a Seifert-Van Kampen theorem is reduced to a purely geometric statement of effective descent. © 2006 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.