Mathematical Research Letters

Volume 23 (2016)

Number 5

Examples of quasitoric manifolds as special unitary manifolds

Pages: 1453 – 1468

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n5.a10

Authors

Zhi Lü (School of Mathematical Sciences, Fudan University, Shanghai, China)

Wei Wang (College of Information Technology, Shanghai Ocean University, Shanghai, China)

Abstract

This note shows that for each $n \geq 5$ with only $n \neq 6$, there exists a $2n$-dimensional specially omni-oriented quasitoric manifold $M^{2n}$ which represents a nonzero element in ${\Omega}^U_{*}$. This provides the counter-examples of Buchstaber–Panov–Ray conjecture.

Keywords

unitary bordism, special unitary manifold, quasitoric manifold, small cover, Stong manifold

2010 Mathematics Subject Classification

Primary 57R85, 57S10. Secondary 14M25, 52B70.

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Published 12 January 2017