Genus-3 Lefschetz Fibrations and Exotic 4-Manifolds with b₂⁺=3

2020/01/27 by Altunoz, Tulin
#57R17 #57R55 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2001.09712

Abstract

We explicitly construct a genus-3 Lefschetz fibration over \mathbbS² whose total space is \mathbbT²× \mathbbS²# 6ℂ P² using the monodromy of Matsumoto's genus-2 Lefschetz fibration. We then construct more genus-3 Lefschetz fibrations whose total spaces are exotic minimal symplectic 4-manifolds 3 ℂ P² # qℂ P² for q=13,…,19. We also generalize our construction to get genus-3k Lefschetz fibration structure on the 4-manifold Σ_k× \mathbbS²# 6ℂ P² using the generalized Matsumoto's genus-2k Lefschetz fibration. From this generalized version, we derive further exotic 4-manifolds via Luttinger surgery and twisted fiber sum.

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