manifolds and cobordisms
cobordism theory, Introduction
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
This page collects material related to the book
Bordism, Stable Homotopy and Adams Spectral Sequences
Fields Institute Monographs
American Mathematical Society, 1996
on cobordism theory, stable homotopy theory, complex oriented cohomology, and the Adams spectral sequence.
From p. 13:
The approach to stable homotopy presented in this book originated with graduate courses taken by the author at the University of Chicago from 1966 to 1970 given by Frank Adams, Arunas Liulevicius and Peter May. The content of the lectures by Adams have been published in $[$Adams: Stable homotopy and generalised homology (1974)$]$. However, the content of the courses given by Liulevicius on bordism and by May on characteristic classes and on the Adams spectral sequence have not been published. Most of the material in the first four chapters has been given by the author as graduate courses at Yale University, Purdue University and the University of Western Ontario.
multiplicative cohomology of $B U(1)$ (prop. 4.3.2, this is lemma 2.5 in part II of John Adams, Stable homotopy and generalised homology)
the computation sketched after “we show that $\pi_1S = Z/2$” is the one that is spelled out for instance in (Bruner 09, pages 2-4)
p. 36, second line: on the right replace $p$ by $p-1$, i.e. replace $\pi_p \colon G^n \to D^{p,n-p}$ by $\pi_{p-1} \colon G^n \to D^{p-1,n-p+1}$ (see end of the proof on the same page)
p. 41, second diagram: the top horizontal moprhism is missing a superscript star.
p. 192, second displayed formula from below: The expression for $Cotor$ on the left has a superfluous argument $A$.
p. 199, the spectral sequence in prop. 5.3.1 converges not to the cobar complex, but to the cohomology of that complex, namely to $Cotor_{\mathcal{A}^\ast}(\mathbb{Z}/2, \mathbb{Z}/2)$ (as shown correctly in the paragraph just before);
p. 199, very last line: $E_0$ must be $E^0$ (not the 0-page of the spectral sequence, but the associated graded module, as defined on p. 198)
Last revised on January 25, 2021 at 15:41:49. See the history of this page for a list of all contributions to it.