The main aim of this paper is the construction of a smooth (sometimes called differential) extension \hat{MU} of the cohomology theory complex cobordism MU, using cycles for \hat{MU}(M) which are essentially proper maps W\to M with a fixed U(n)-structure and U(n)-connection on the (stable) normal bundle of W\to 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, using the Landweber exact functor principle, that \hat{R}(M):=\hat{MU}(M)\otimes_{MU^*}R defines a multiplicative smooth extension of R(M):=MU(M)\otimes_{MU^*}R whenever R is a Landweber exact MU*-module. An example for this construction is a new way to define a multiplicative smooth K-theory
我们引入了一类新的自然的，明确定义的，横向椭圆微分算过流形紧群的行动。在一定条件下，这些运营商的符号生成等变指数的所有可能的值。我们还表明，该表示值等变指数的成分与那些从原始数据构造的椭圆算子的一致。
代数和几何拓扑的目的是数学的进步。编辑评价提交的论文严格科学的优点的基础上，不考虑作者的国籍，居住国，所属机构，性别，族裔和政治
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