Circle actions on 8-dimensional almost complex manifolds with 4 fixed points

In this paper, we prove that if the circle acts on an 8-dimensional compact almost complex manifold M with 4 fixed points, all the Chern numbers and the Hirzebruch χ y -genus of M agree with those of S 2 × S 6 . In particular, M is unitary cobordant to S 2 × S 6 .

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Bibliographic Details
Published inJournal of fixed point theory and applications Vol. 22; no. 4
Main Author Jang, Donghoon
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2020
Subjects
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Secondary 37C25
circle action
fixed point
37C55
weight
Primary 58C30
Almost complex manifold
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Summary:In this paper, we prove that if the circle acts on an 8-dimensional compact almost complex manifold M with 4 fixed points, all the Chern numbers and the Hirzebruch χ y -genus of M agree with those of S 2 × S 6 . In particular, M is unitary cobordant to S 2 × S 6 .
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-020-00823-3