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2013•DuEPublico (University of Duisburg-Essen)Open access

Homotopy Sequence for Fundamental Groups

Lei Zhang

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Abstract

In SGA 1, A.Grothendieck developped the notion of etale fundamental group which is a generalization of the Galois group. And he further studied the homotopy sequence associated to a fibration of schemes. In this thesis we study the corresponding homotopy sequence for two generalizations of the etale fundamental group--- the Nori's fundamental group and the algebraic fundamental group.

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In SGA 1, A.Grothendieck developped the notion of etale fundamental group which is a generalization of the Galois group. And he further studied the homotopy sequence associated to a fibration of schemes. In this thesis we study the corresponding homotopy sequence for two generalizations of the etale fundamental group--- the Nori's fundamental group and the algebraic fundamental group.

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Available abstract

In SGA 1, A.Grothendieck developped the notion of etale fundamental group which is a generalization of the Galois group. And he further studied the homotopy sequence associated to a fibration of schemes. In this thesis we study the corresponding homotopy sequence for two generalizations of the etale fundamental group--- the Nori's fundamental group and the algebraic fundamental group.

Key concepts: Homotopy group, Fundamental group, Mathematics, Sequence (biology), Group (periodic table), Exact sequence, n-connected, Fibration

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