Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SIX DIMENSIONAL ALMOST COMPLEX TORUS MANIFOLDS WITH EULER NUMBER SIX

  • Donghoon Jang (Department of Mathematics Pusan National University) ;
  • Jiyun Park (Department of Mathematics Pusan National University)
  • Received : 2023.04.11
  • Accepted : 2023.08.29
  • Published : 2024.03.31
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Abstract

An almost complex torus manifold is a 2n-dimensional compact connected almost complex manifold equipped with an effective action of a real n-dimensional torus Tn ≃ (S1)n that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let M be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for M, and for each type of graph we construct such a manifold M, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch χy-genus of M.

Keywords

Acknowledgement

Donghoon Jang was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2021R1C1C1004158).

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