2020/05/21 by Arijit Nath, Nath, Arijit, Kuldeep Saha +1
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2005.10772
We discuss embedding of manifolds in the category of open books, contact manifolds and contact open books. We prove an open book version of the Haefliger--Hirsch embedding theorem by showing that every k-connected closed n-manifold (n≥ 7, k < (n-4)/(2)) admits an open book embedding in the trivial open book of \mathbbS2n-k. We then prove that every closed manifold M2n+1 that bounds an achiral Lefschetz fibration, admits open book embedding in the trivial open book of \mathbbS2\lfloor(3n)/(2)\rfloor + 3. We also prove that every closed manifold M2n+1 bounding an achiral Lefschetz fibration admits a contact structure that isocontact embeds in the standard contact structure on ℝ2n+3. Finally, we give various examples of contact open book embeddings of contact (2n+1)-manifolds in the trivial supporting open book of the standard contact structure on \mathbbS4n+1.