Connected sums of almost complex manifolds

2018/08/22 by Yang, Huijun
#53C15 #55S35 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1808.07343

Abstract

In this paper, firstly, for some 4n-dimensional almost complex manifolds M_i, ~1≤ i ≤ α, we prove that (\sharp_i=1^α M_i) \sharp (α-1) ℂ P²ⁿ must admits an almost complex structure, where α is a positive integer. Secondly, for a 2n-dimensional almost complex manifold M, we get that M\sharp ℂ Pⁿ also admits an almost complex structure. At last, as an application, we obtain that αℂ P²ⁿ\sharp βℂ P²ⁿ admits an almost complex structure if and only if α is odd.

Related

• Connected sums of almost complex manifolds, products of rational homology spheres, and the twisted spin^c Dirac operator
• Almost Complex Structures on (n-1)-connected 2n-manifolds
• Almost complex blow-ups and positive closed (1,1)-forms on 4-dimensional almost complex manifolds
• Almost Complex Structures on Homotopy Complex Projective Spaces
• Almost complex Hodge theory