Original Articles

ON A KERVAIRE DIAGRAM FOR A HOMOTOPY PULLBACK OF GROUPOIDS

Published in: Quaestiones Mathematicae
Volume 10 , issue 1 , 1986 , pages: 63–81

DOI: 10.1080/16073606.1986.9631592

Author(s): K.A. Hardie Department of Mathematics, South Africa , K.H. Kamps , Fed. Rep. of Germany

Keywords: 20L15 , 18G50 , 55405 , 55Q35 , 55537 , 20L10

Abstract

A Kervaire diagram of group homomorphisms and pointed maps arising from a standard homotopy pullback Z of groupoid morphisms with common codomain is studied. The diagram yields two exact Mayer-Vietoris sequences that specialize in various ways. A classification theorem is obtained for the set of components of z. Applications are given to elementary group theory and to homotopy pair theory.

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