AN ORLIK-RAYMOND TYPE CLASSIFICATION OF SIMPLY CONNECTED 6-DIMENSIONAL TORUS MANIFOLDS WITH VANISHING ODD-DEGREE COHOMOLOGY

作者：Kuroki Shintaro^*

来源：Pacific Journal of Mathematics, 2016, 280(1): 89-114.

DOI：10.2140/pjm.2016.280.89

• torus manifold
• torus graph
• GKM graph
• equivariant connected sum

The aim of this paper is to classify simply connected 6-dimensional torus manifolds with vanishing odd-degree cohomology. It is shown that there is a one-to-one correspondence between equivariant diffeomorphism types of these manifolds and 3-valent labelled graphs, called torus graphs, introduced by Maeda, Masuda and Panov. Using this correspondence and combinatorial arguments, we prove that a simply connected 6-dimensional torus manifold with H-odd(M) = 0 is equivariantly diffeomorphic to the 6-dimensional sphere S-6 or an equivariant connected sum of copies of 6-dimensional quasitoric manifolds or S-4-bundles over S-2.

• 出版日期2016-1