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1998 Flag manifolds and the Landweber–Novikov algebra
Victor M Buchstaber, Nigel Ray
Geom. Topol. 2(1): 79-101 (1998). DOI: 10.2140/gt.1998.2.79


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.


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Victor M Buchstaber. Nigel Ray. "Flag manifolds and the Landweber–Novikov algebra." Geom. Topol. 2 (1) 79 - 101, 1998.


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

zbMATH: 0907.57025
MathSciNet: MR1623426
Digital Object Identifier: 10.2140/gt.1998.2.79

Primary: 57R77
Secondary: 14M15, 14M25, 55S25

Rights: Copyright © 1998 Mathematical Sciences Publishers


Vol.2 • No. 1 • 1998
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