可逆$2维框架和$r$自旋拓扑场论

IF 0.8 4区数学 Q2 MATHEMATICS Homology Homotopy and Applications Pub Date : 2023-01-01 DOI:10.4310/hha.2023.v25.n1.a6

Lóránt Szegedy

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引用次数: 0

摘要

通过计算可逆二维框架和r自旋拓扑场论的同伦群和相应的界域范畴的k不变量，对它们进行了分类。根据Kreck, Stolz和Teichner最近的结果，第一个同伦群是由所谓的SKK群给出的。我们使用Novak, Runkel和作者的框架和$r$自旋曲面的组合模型显式地计算了它们。

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On invertible $2$-dimensional framed and $r$-spin topological field theories

We classify invertible 2-dimensional framed and $r$-spin topological field theories by computing the homotopy groups and the $k$-invariant of the corresponding bordism categories. By a recent result of Kreck, Stolz and Teichner the first homotopy groups are given by the so called SKK groups. We compute them explicitly using the combinatorial model of framed and $r$-spin surfaces of Novak, Runkel and the author.

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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.

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