Bunke, Ulrich and Schick, Thomas and Schroeder, Ingo and Wiethaup, Moritz (2009) Landweber exact formal group laws and smooth cohomology theories. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 9 (3). pp. 1751-1790. ISSN 1472-2739,
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The main aim of this paper is the construction of a smooth ( sometimes called differential) extension (MU) over cap of the cohomology theory complex cobordism MU, using cycles for (MU) over cap (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 (R) over cap (M): = (MU) over cap (M)circle times(MU*) R defines a multiplicative smooth extension of R(M): = MU(M)circle times(MU*) R 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DELIGNE COHOMOLOGY; GEOMETRY; TOPOLOGY; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Oct 2020 04:54 |
| Last Modified: | 12 Oct 2020 04:54 |
| URI: | https://pred.uni-regensburg.de/id/eprint/29606 |
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