Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori, II

Creators: Ni, Yi

Abstract

We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S^2×S^1 or ℝP^3#ℝP^3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni (2014) in an earlier paper.

Additional Information

© 2017 Science China Press and Springer-Verlag Berlin Heidelberg. Received December 23, 2016; accepted March 6, 2017. First Online: 07 April 2017. Dedicated to Professor Boju Jiang on the Occasion of His 80th Birthday. This work was supported by National Science Foundation of USA (Grant No. DMS-1252992) and an Alfred P. Sloan Research Fellowship. The author thanks a referee for clarifying some arguments in geometric group theory.

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Resource type: Journal Article
Publisher: Springer
Published in: Science China Mathematics, 60(9), 1591-1598, ISSN: 1674-7283.

Created:: August 19, 2023
Modified:: October 25, 2023