ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 55 Tamanoi, Hirotaka, University of California Santa Cruz, USA BP cohomology theory and v_{n}-series We introduce BP topology which is the most natural topology on Brown-Peterson (BP) cohomology groups: it is always Hausdorff for any space, and relations expressed as convergent infinite sums can be studied. In BP theory, the p-series has played an important role. We introduce its generalization, v_{n}-series for all n ≥ 0, as certain elements in BP cohomology of Ω-spectrum of BP theory. These v_{n}-series measure noncommutative nature of the splittings of the Ω-spectrum in critical degrees. We will also discuss applications of v_{n}-series to the structure of BP cohomology theory.