Bott cannibalistic class

In mathematics, the Bott cannibalistic class, introduced by Raoul Bott (1962), is an element ${\displaystyle \theta _{k}(V)}$ of the representation ring of a compact Lie group that describes the action of the Adams operation ${\displaystyle \psi ^{k}}$ on the Thom class ${\displaystyle \lambda _{V}}$ of a complex representation ${\displaystyle V}$. The term "cannibalistic" for these classes was introduced by Frank Adams (1965, p.151).

References

• Adams, J. Frank (1965), "On the groups ${\displaystyle J(X)}$. II.", Topology, 3 (2): 137–171, doi:10.1016/0040-9383(65)90040-6, MR 0198468
• Bott, Raoul (1962), "A note on the KO-theory of sphere-bundles", Bulletin of the American Mathematical Society, 68: 395–400, doi:10.1090/S0002-9904-1962-10819-2, ISSN 0002-9904, MR 0153019