Geometry & Topology

Flag manifolds and the Landweber–Novikov algebra

Victor M Buchstaber and Nigel Ray

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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

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

Received: 23 October 1997
Revised: 6 January 1998
Accepted: 1 June 1998
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R77: Complex cobordism (U- and SU-cobordism) [See also 55N22]
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14M25: Toric varieties, Newton polyhedra [See also 52B20] 55S25: $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]

complex cobordism double cobordism flag manifold Schubert calculus toric variety Landweber–Novikov algebra


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.

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