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.