An Orlik-Raymond type classification of simply connected six-dimensional torus manifolds with vanishing odd degree cohomology
arXiv:1305.3174 · doi:10.2140/pjm.2016.280.89
Abstract
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-Panov. Using this correspondence and combinatorial arguments, we prove that a simply connected 6-dimensional torus manifold with vanishing odd degree cohomology is equivariantly diffeomorphic to the 6-dimensional sphere or an equivariant connected sum of copies of 6-dimensional quasitoric manifolds or 4-dimensional sphere bundles over the 2-dimensional sphere.
18 pages, 11 figures, v2: minor changes, v3: change the definition of equivariant connected sum, v4: replacing the previous version