Volume 16, issue 5 (2016)

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On toric generators in the unitary and special unitary bordism rings

Zhi Lü and Taras Panov

Algebraic & Geometric Topology 16 (2016) 2865–2893

We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also construct a family of special unitary quasitoric manifolds which contains polynomial generators of the special unitary bordism ring with 2 inverted in dimensions > 8. Each manifold in the latter family is obtained from an iterated complex projectivisation of a sum of line bundles by amending the complex structure to make the first Chern class vanish.

complex bordism, SU-bordism, toric manifold, characteristic numbers
Mathematical Subject Classification 2010
Primary: 57R77
Secondary: 14M25
Received: 2 June 2015
Revised: 15 October 2015
Accepted: 20 February 2016
Published: 7 November 2016
Zhi Lü
School of Mathematical Sciences
Fudan University
Shanghai, 200433, China
Taras Panov
Department of Mathematics and Mechanics
Moscow State University
Leninskie Gory, Moscow, 119991, Russia
Institute for Theoretical and Experimental Physics
Main Cheremushkinskaya St, Moscow 117218, Russia
Institute for Information Transmission Problems, Russian Academy of Sciences
Bolshoy Karetny Lane, Moscow 127051, Russia