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"This book is a jewel- it explains important, useful and deep
topics in Algebraic Topology that you won't find elsewhere,
carefully and in detail." Prof. Gunter M. Ziegler, TU Berlin
These notes were taken from lectures given by tom Dieck in the win-
ter-term 1969/70 at the Mathematical Institute in Heidelberg. The
aim of the lectures was to introduce the students to cobordism
theory and to propagate ideas of Boardman and Quillen about the
calculation of cobordism theories with the aid of formal groups.
These notes give an enlarged version of the leetures with many
details and proofs filled in. A chapter on unitary cobordism has
been left out and will appear separately. The eontents of the notes
are as follows: In chapter I we recall those parts of differential
topology and of the theory of veetor bundles which we will use.
This only to re- wind the reader of well known faets or to give
hints at neeessary pre- requisites to students willing to learn
differential topology. Apart from these faets we assume knowledge
of elementary homotopy theory and classical cohomology with
coefficients in l2, characterized by the Eilenberg-Steenrod axioms.
In chapter II the (non oriented) bordism homology theory N.(-) is
defined by singular manifolds. We verify the axioms of a homology
theory. Our approach differs from that of Conner and Floyd [4] in
that we only define absolute homology groups and use a system of
axioms in which an exact sequence of Mayer-Vietoris type plays the
main role.
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