## Geometry & Topology

### Flag manifolds and the Landweber–Novikov algebra

#### Abstract

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 Poincaré duality with respect to double cobordism theory; these lead directly to our main results for the Landweber–Novikov algebra.

#### Article information

Source
Geom. Topol., Volume 2, Number 1 (1998), 79-101.

Dates
Revised: 6 January 1998
Accepted: 1 June 1998
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882903

Digital Object Identifier
doi:10.2140/gt.1998.2.79

Mathematical Reviews number (MathSciNet)
MR1623426

Zentralblatt MATH identifier
0907.57025

#### Citation

Buchstaber, Victor M; Ray, Nigel. Flag manifolds and the Landweber–Novikov algebra. Geom. Topol. 2 (1998), no. 1, 79--101. doi:10.2140/gt.1998.2.79. https://projecteuclid.org/euclid.gt/1513882903

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