光滑和接触歧管的开卷和嵌入

IF 0.5 4区 数学 Q3 MATHEMATICS
Arijit Nath, Kuldeep Saha
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引用次数: 0

摘要

讨论了在开放书、Lefschetz振动、接触流形和接触开放书等类别下的嵌入结果。首先,我们证明了Haefliger-Hirsch嵌入定理的一个开卷版本,证明了每一个签名为0的k连通的闭n流形(n≥7,k < (n−4)/2)在平凡的𝕊2n−k的开卷中都有一个开卷嵌入。然后,我们证明了在非手性Lefschetz纤维的边界上的每一个闭流形M2n+1都允许一个开卷嵌入在平凡的开卷𝕊2中⌊3n/2⌋+3。我们还证明了每一个封闭流形M2n+1边界上的非手性Lefschetz振动都存在一个等接触嵌入在标准接触结构中的接触结构。最后,我们给出了在𝕊4n+1上标准接触结构的平凡支撑开卷中接触(2n +1)流形的接触开卷嵌入的各种例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Open books and embeddings of smooth and contact manifolds
Abstract We discuss some embedding results in the category of open books, Lefschetz fibrations, contact manifolds and contact open books. First 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) with signature zero admits an open book embedding in the trivial open book of 𝕊2n−k. We then prove that every closed manifold M2n+1 that bounds an achiral Lefschetz fibration admits an open book embedding in the trivial open book of 𝕊2⌊3n/2⌋+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 𝕊4n+1.
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来源期刊
Advances in Geometry
Advances in Geometry 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
31
审稿时长
>12 weeks
期刊介绍: Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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