关于李群的串拓扑协积

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2021-09-21 DOI:10.4310/hha.2022.v24.n2.a17

Maximilian Stegemeyer

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引用次数: 2

摘要

李群的自由环空间同胚于李群本身及其基环空间的乘积。我们证明了由Goresky和Hingston引入的自由环空间的同调上的余积分裂成群上的对角映射和基环空间的同源上的所谓基余积。这一结果表明，对于偶数维李群，协积是平凡的。利用Bott和Samelson的结果，我们证明了对于一个大的单连通李群族，协积也是平凡的。内容

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On the string topology coproduct for Lie groups

The free loop space of a Lie group is homeomorphic to the product of the Lie group itself and its based loop space. We show that the coproduct on the homology of the free loop space that was introduced by Goresky and Hingston splits into the diagonal map on the group and a so-called based coproduct on the homology of the based loop space. This result implies that the coproduct is trivial for even-dimensional Lie groups. Using results by Bott and Samelson, we show that the coproduct is trivial as well for a large family of simply connected Lie groups. CONTENTS

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.