Computation of KO characteristic classes/numbers - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T00:51:26Z http://mathoverflow.net/feeds/question/99894 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99894/computation-of-ko-characteristic-classes-numbers Computation of KO characteristic classes/numbers Paul Meier 2012-06-18T12:50:47Z 2012-06-18T13:18:24Z <p>How to compute KO characteristic classes/numbers?</p> <p>They were introduced by Anderson/Brown/Peterson to study the structure of the spin cobordism ring. I looked through the literature but I did not find a nice example of computation. For instance, I would like to know how to determine $\pi^J(\mathbb{H}P^2)$. Many thanks for any comments in advance. </p> http://mathoverflow.net/questions/99894/computation-of-ko-characteristic-classes-numbers/99896#99896 Answer by Mark Grant for Computation of KO characteristic classes/numbers Mark Grant 2012-06-18T13:18:24Z 2012-06-18T13:18:24Z <p>Chapter II (in particular sections II.7 and II.9) of the book</p> <p>Conner, P. E.; Floyd, E. E. The relation of cobordism to K-theories. Lecture Notes in Mathematics, No. 28 Springer-Verlag, Berlin-New York 1966 v+112 pp. </p> <p>gives a nice construction of $KO$-characteristic classes for symplectic bundles, in particular showing that they satisfy the usual axioms. From this you may be able to perform computations. I'm not sure what the notation $\pi^J$ means (cokernel of the J-homomorphism?).</p>