2009
DOI: 10.2140/agt.2009.9.1751
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Landweber exact formal group laws and smooth cohomology theories

Abstract: The main aim of this paper is the construction of a smooth (sometimes called differential) extension b MU of the cohomology theory complex cobordism MU , using cycles for bMU .M / which are essentially proper maps W ! M with a fixed U -structure and U -connection on the (stable) normal bundle of W ! M .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 y R.M / WD b MU .M /… Show more

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Cited by 17 publications
(35 citation statements)
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“…Now we define the cycles of our differential cohomology following the recipe as for for singular cobordism [4]. The starting point is the description of k-th ordinary integral cohomology of X as bordism classes of continuous oriented proper maps from oriented regular stratifolds S of dimension (n − k) to X [11,Chapter 12].…”
Section: Differential Cohomology Via Stratifoldsmentioning
confidence: 99%
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“…Now we define the cycles of our differential cohomology following the recipe as for for singular cobordism [4]. The starting point is the description of k-th ordinary integral cohomology of X as bordism classes of continuous oriented proper maps from oriented regular stratifolds S of dimension (n − k) to X [11,Chapter 12].…”
Section: Differential Cohomology Via Stratifoldsmentioning
confidence: 99%
“…The proof that these maps are well defined is literally the same as in the case, where we have smooth manifolds instead of stratifolds [4,Lemma 4.10], since the basic ingredient, Stokes' Theorem, is available.…”
Section: Differential Cohomology Via Stratifoldsmentioning
confidence: 99%
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