Almost complex structure and the quotient four-manifold by an anti-symplectic involution

作者：Cho Yong Seung^*; Hong Yoon Hi

来源：Topology and Its Applications, 2010, 157(2): 385-392.

DOI：10.1016/j.topol.2009.09.007

• Anti-symplectic involution
• Symplectic four-manifold
• Almost complex structure
• Lagrangian surface
• Quotient manifold

Suppose that X is a closed, symplectic four-manifold with an anti-symplectic involution a and its two-dimensional fixed point set. We show that the quotient X/sigma admits no almost complex structure if b(2)(+)(X) not equivalent to b(1) (X) + 3 mod 4.
As a partial converse if X is simply-connected and b(2)(+) (X) equivalent to 3 mod 4, then the X/sigma admits an almost complex structure.
Also we show that the quotient X/sigma admits an almost complex structure if X is Kahler and b(2)(+) (X) equivalent to b(1) (X) + 3 mod 4.

• 出版日期2010-2-1