{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BBBEZTY3HVICFWRNAJDTANPIX7","short_pith_number":"pith:BBBEZTY3","schema_version":"1.0","canonical_sha256":"08424ccf1b3d5022da2d02473035e8bffd4c0ddd3da7fddb2e017f713eecce4b","source":{"kind":"arxiv","id":"1507.00597","version":2},"attestation_state":"computed","paper":{"title":"A note on torus actions and the Witten genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Michael Wiemeler","submitted_at":"2015-07-02T14:17:48Z","abstract_excerpt":"We show that the Witten genus of a string manifold $M$ vanishes, if there is an effective action of a torus $T$ on $M$ such that $\\dim T>b_2(M)$. We apply this result to study group actions on $M\\times G/T$, where $G$ is a compact connected Lie group and $T$ a maximal torus of $G$.\n Moreover, we use the methods which are needed to prove these results to the study of torus manifolds. We show that up to diffeomorphism there are only finitely many quasitoric manifolds $M$ with the same cohomology ring as $#_{i=1}^k \\pm\\mathbb{C} P^n$ with $kb_2(M)$. We apply this result to study group actions on $M\\times G/T$, where $G$ is a compact connected Lie group and $T$ a maximal torus of $G$.\n Moreover, we use the methods which are needed to prove these results to the study of torus manifolds. We show that up to diffeomorphism there are only finitely many quasitoric manifolds $M$ with the same cohomology ring as $#_{i=1}^k \\pm\\mathbb{C} P^n$ with $k