Mathematical Research Letters

Volume 27 (2020)

Number 3

From automorphisms of Riemann surfaces to smooth $4$-manifolds

Pages: 629 – 645

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n3.a1

Authors

Ahmet Beyaz (Department of Mathematics, Middle East Technical University, Ankara, Turkey)

Patrick Naylor (Department of Pure Mathematics, University of Waterloo, Ontario, Canada)

Sinem Onaran (Department of Mathematics, Hacettepe University, Ankara, Turkey)

B. Doug Park (Department of Pure Mathematics, University of Waterloo, Ontario, Canada)

Abstract

Starting from a suitable set of self-diffeomorphisms of a closed Riemann surface, we present a general branched covering method to construct surface bundles over surfaces with positive signature. Armed with this method, we study the classification problem for both surface bundles with nonzero signature and closed simply connected smooth $\operatorname{spin} 4$-manifolds.

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The first author was a Fulbright visiting scholar at Harvard University during part of this work. He thanks İnanç Baykur for helpful discussions. The second author was partially supported by an NSERC CGS-D scholarship. The third author was partially supported by Turkish Academy of Sciences ÏUBA-GEBİP. The fourth author was partially supported by an NSERC discovery grant.

Received 6 July 2018

Accepted 6 January 2019

Published 20 August 2020