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Six dimensional almost complex torus manifolds with Euler number six

Authors :
Jang, Donghoon
Park, Jiyun
Source :
Bulletin of the Korean Mathematical Society, 61 (2024), 557-584
Publication Year :
2023

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 $T^n \simeq (S^1)^n$ 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 $\chi_y$-genus of $M$.

Details

Database :
arXiv
Journal :
Bulletin of the Korean Mathematical Society, 61 (2024), 557-584
Publication Type :
Report
Accession number :
edsarx.2303.11618
Document Type :
Working Paper
Full Text :
https://doi.org/10.4134/BKMS.b230227