Volume 2, issue 1 (1998)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Flag manifolds and the Landweber–Novikov algebra

Victor M Buchstaber and Nigel Ray

Geometry & Topology 2 (1998) 79–101

arXiv: math.AT/9806168

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.

Keywords
complex cobordism, double cobordism, flag manifold, Schubert calculus, toric variety, Landweber–Novikov algebra
Mathematical Subject Classification
Primary: 57R77
Secondary: 14M15, 14M25, 55S25
References
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Publication
Received: 23 October 1997
Revised: 6 January 1998
Accepted: 1 June 1998
Published: 3 June 1998
Proposed: Haynes Miller
Seconded: Gunnar Carlsson, Ralph Cohen
Authors
Victor M Buchstaber
Department of Mathematics and Mechanics
Moscow State University
119899 Moscow
Russia
Nigel Ray
Department of Mathematics
University of Manchester
Manchester
M13 9PL
United Kingdom