On the map of Bökstedt–Madsen from the cobordism category to A–theory
On the map of Bökstedt–Madsen from the cobordism category to A–theory
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在 Bökstedt-Madsen 地图上从共边主义类别到 A 理论
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
W. Steimle
中科院分区：
文献类型：
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作者：
G. Raptis;W. Steimle
Bokstedt和Madsen定义了一个从Galatius， Madsen， Tillmann和Weiss的嵌入d维协同范畴到BO的代数K理论的无限循环映射。d/ Waldhausen的意思。本文的目的是建立与此图相关的两个结果。第一个结果是，它扩展了Dwyer， Weiss和Williams定义的具有紧致d维纤维的光滑束的普遍参数化A -理论欧拉特性。第二个结果是，它实际上是通过规范单元映射Q.BO.d/C/！A.BO.d / /。19d10, 55r12, 57r90
Bokstedt and Madsen defined an infinite loop map from the embedded d‐dimensional cobordism category of Galatius, Madsen, Tillmann and Weiss to the algebraic K‐ theory of BO.d/ in the sense of Waldhausen. The purpose of this paper is to establish two results in relation to this map. The first result is that it extends the universal parametrized A‐theory Euler characteristic of smooth bundles with compact d‐ dimensional fibers, as defined by Dwyer, Weiss and Williams. The second result is that it actually factors through the canonical unit map Q.BO.d/C/! A.BO.d//. 19D10, 55R12, 57R90