Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 9, Number 3 (2009), 1751-1790.
Landweber exact formal group laws and smooth cohomology theories
The main aim of this paper is the construction of a smooth (sometimes called differential) extension of the cohomology theory complex cobordism , using cycles for which are essentially proper maps with a fixed –structure and –connection on the (stable) normal bundle of .
Crucial is that this model allows the construction of a product structure and of pushdown maps for this smooth extension of , which have all the expected properties.
Moreover, we show that defines a multiplicative smooth extension of whenever is a Landweber exact –module, by using the Landweber exact functor principle. An example for this construction is a new way to define a multiplicative smooth –theory.
Algebr. Geom. Topol., Volume 9, Number 3 (2009), 1751-1790.
Received: 24 September 2008
Revised: 15 July 2009
Accepted: 19 July 2009
First available in Project Euclid: 20 December 2017
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Bunke, Ulrich; Schick, Thomas; Schröder, Ingo; Wiethaup, Moritz. Landweber exact formal group laws and smooth cohomology theories. Algebr. Geom. Topol. 9 (2009), no. 3, 1751--1790. doi:10.2140/agt.2009.9.1751. https://projecteuclid.org/euclid.agt/1513797043