乌姆凯尔地图
Umkehr Maps
摘要：
在这篇笔记中，我们研究了广义（co）同调论中的umkehr映射，这些理论来自于Pontrjagin-Thom构造，沿着纤维积分，推进同态和其他类似的构造。我们认为这些建设的基本性质和发展公理，任何umkehr同态必须满足。我们使用一个版本的布朗表示，这些公理完全刻画这些同态，并由此产生的唯一性定理如下。最后，出于弦拓扑结构，我们扩展了这种公理化的治疗umkehr同态的fiberwise设置。
英文摘要：
In this note we study umkehr maps in generalized (co)homology theories arising from the Pontrjagin-Thom construction, from integrating along fibers, pushforward homomorphisms, and other similar constructions. We consider the basic properties of these constructions and develop axioms which any umkehr homomorphism must satisfy. We use a version of Brown representability to show that these axioms completely characterize these homomorphisms, and a resulting uniqueness theorem follows. Finally, motivated by constructions in string topology, we extend this axiomatic treatment of umkehr homomorphisms to a fiberwise setting.
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