Flag manifolds and the Landweber-Novikov algebra

Details Flag manifolds and the Landweber-Novikov algebra Flag manifolds and the Landweber-Novikov algebra

1998-06-03

arxiv.org/abs/math/9806168v1

Geom. Topol. 2 (1998), 79-101

Mathematics

Algebraic Topology

23 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper5.abs.html

Scientific paper

We investigate geometrical interpretations of various structure maps associated with the Landweber-Novikov algebra S^* and its integral dual S_*. In particular, we study the coproduct and antipode in S_*, together with the left and right actions of S^* on S_* which underly the construction of the quantum (or Drinfeld) double D(S^*). We set our realizations in the context of double complex cobordism, utilizing certain manifolds of bounded flags which generalize complex projective space and may be canonically expressed as toric varieties. We discuss their cell structure by analogy with the classical Schubert decomposition, and detail the implications for Poincare duality with respect to double cobordism theory; these lead directly to our main results for the Landweber-Novikov algebra.

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