Note on new symplectic 4-manifolds with nonnegative signature

Anar Akhmedov

Note on new symplectic 4-manifolds with nonnegative signature

Geometric Topology 2012-07-10 v1 Algebraic Geometry Symplectic Geometry

Authors: Anar Akhmedov

Abstract

In this short note, we present a construction of new symplectic 4-manifolds with non-negative signature using the complex surfaces on Bogomolov-Miyaoka-Yau line $c_1^2 = 9\chi_h$ , the fake projective planes and Cartwright-Steger surfaces. Our construction yields an infinite family of fake rational homology $(2n-1)\CP#(2n-1)\CPb$ for any integer $3 \leq n \leq 22$ .

Keywords

symplectic 4-manifolds nonnegative signature bogomolov-miyaoka-yau line fake projective planes cartwright-steger surfaces rational homology complex surfaces

Cite

@article{arxiv.1207.1973,
  title  = {Note on new symplectic 4-manifolds with nonnegative signature},
  author = {Anar Akhmedov},
  journal= {arXiv preprint arXiv:1207.1973},
  year   = {2012}
}

Comments

9 pages, 1 figure

Related papers

View all related →

Symplectic Geometry · Mathematics

Complex Ball Quotients and New Symplectic 4-manifolds with Nonnegative Signatures