Mathematical Research Letters

Volume 23 (2016)

Number 5

Examples of quasitoric manifolds as special unitary manifolds

Pages: 1453 – 1468



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

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


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.


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

2010 Mathematics Subject Classification

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

Accepted 22 February 2015

Published 12 January 2017