渐近平坦Fredholm束与集合

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2023-11-10 DOI:10.1142/s1793525323500413

Benedikt Hunger

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引用次数: 0

摘要

Hanke和Schick成功地利用几乎平坦有限生成的射影Hilbert C*模束证明了强诺维科夫猜想的特殊情况。Dadarlat后来证明了可以根据Lafforgue集合映射下的$\eta$像和与该束相关联的几乎表示来计算K_*(M)$扭曲中的k -同调类$\eta\的索引。为了证明Novikov高签名猜想的特殊情况，Mishchenko使用了配备Fredholm算子的平面无限维束。

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Asymptotically Flat Fredholm Bundles and Assembly

Almost flat finitely generated projective Hilbert C*-module bundles were successfully used by Hanke and Schick to prove special cases of the Strong Novikov Conjecture. Dadarlat later showed that it is possible to calculate the index of a K-homology class $\eta\in K_*(M)$ twisted with an almost flat bundle in terms of the image of $\eta$ under Lafforgue's assembly map and the almost representation associated to the bundle. Mishchenko used flat infinite-dimensional bundles equipped with a Fredholm operator in order to prove special cases of the Novikov higher signature conjecture.

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.