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2009 Landweber exact formal group laws and smooth cohomology theories
Ulrich Bunke, Thomas Schick, Ingo Schröder, Moritz Wiethaup
Algebr. Geom. Topol. 9(3): 1751-1790 (2009). DOI: 10.2140/agt.2009.9.1751


The main aim of this paper is the construction of a smooth (sometimes called differential) extension MÛ of the cohomology theory complex cobordism MU, using cycles for MÛ(M) which are essentially proper maps WM with a fixed U–structure and U–connection on the (stable) normal bundle of WM.

Crucial is that this model allows the construction of a product structure and of pushdown maps for this smooth extension of MU, which have all the expected properties.

Moreover, we show that R̂(M):=MÛ(M)MUR defines a multiplicative smooth extension of R(M):=MU(M)MUR whenever R is a Landweber exact MU–module, by using the Landweber exact functor principle. An example for this construction is a new way to define a multiplicative smooth K–theory.


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Ulrich Bunke. Thomas Schick. Ingo Schröder. Moritz Wiethaup. "Landweber exact formal group laws and smooth cohomology theories." Algebr. Geom. Topol. 9 (3) 1751 - 1790, 2009.


Received: 24 September 2008; Revised: 15 July 2009; Accepted: 19 July 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1181.55006
MathSciNet: MR2550094
Digital Object Identifier: 10.2140/agt.2009.9.1751

Primary: 55N20, 57R19

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.9 • No. 3 • 2009
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