Almost complex manifolds with total Betti number three

2021/08/13 by Hu, Jiahao
#32Q60 #53C15 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.06067

Abstract

We show the minimal total Betti number of a closed almost complex manifold of dimension 2n≥ 8 is four, thus confirming a conjecture of Sullivan except for dimension 6. Along the way, we prove the only simply connected closed complex manifold having total Betti number three is the complex projective plane.

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