On toric generators in the unitary and special unitary bordism rings

Lü, Zhi; Panov, Taras

doi:10.2140/agt.2016.16.2865

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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

DOI: 10.2140/agt.2016.16.2865

Abstract

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.

Keywords

complex bordism, SU-bordism, toric manifold, characteristic numbers

Mathematical Subject Classification 2010

Primary: 57R77

Secondary: 14M25

References

Publication

Received: 2 June 2015

Revised: 15 October 2015

Accepted: 20 February 2016

Published: 7 November 2016

Authors

Zhi Lü
School of Mathematical Sciences Fudan University Shanghai, 200433, China
http://homepage.fudan.edu.cn/zhilu/
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
http://higeom.math.msu.su/people/taras/

Volume 16, issue 5 (2016)