关于接触流形的结合和

arXiv - MATH - Geometric Topology Pub Date : 2024-09-09 DOI:arxiv-2409.05612

Miguel Orbegozo Rodriguez

{"title":"关于接触流形的结合和","authors":"Miguel Orbegozo Rodriguez","doi":"arxiv-2409.05612","DOIUrl":null,"url":null,"abstract":"In this short note, we give examples of binding sums of contact 3-manifolds\nthat do not preserve properties such as tightness or symplectic fillability. We\nalso prove vanishing of the Heegaard Floer contact invariant for an infinite\nfamily of binding sums where the summands are Stein fillable. This recovers a\nresult of Wendl and Latschev-Wendl. Along the way, we rectify a subtle\ncomputational error in a paper of Juhasz-Kang concerning the spectral order of\na neighbourhood of a Giroux torsion domain.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On binding sums of contact manifolds\",\"authors\":\"Miguel Orbegozo Rodriguez\",\"doi\":\"arxiv-2409.05612\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this short note, we give examples of binding sums of contact 3-manifolds\\nthat do not preserve properties such as tightness or symplectic fillability. We\\nalso prove vanishing of the Heegaard Floer contact invariant for an infinite\\nfamily of binding sums where the summands are Stein fillable. This recovers a\\nresult of Wendl and Latschev-Wendl. Along the way, we rectify a subtle\\ncomputational error in a paper of Juhasz-Kang concerning the spectral order of\\na neighbourhood of a Giroux torsion domain.\",\"PeriodicalId\":501271,\"journal\":{\"name\":\"arXiv - MATH - Geometric Topology\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.05612\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05612","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

在这篇短文中，我们举例说明了不保留紧密性或交点可填充性等性质的接触 3-manifold的约束和。我们还证明了和为 Stein 可填充的无限束缚和族的 Heegaard Floer 接触不变式的消失。这恢复了 Wendl 和 Latschev-Wendl 的结果。在此过程中，我们纠正了 Juhasz-Kang 的一篇论文中关于 Giroux 扭转域邻域谱阶的微妙计算错误。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On binding sums of contact manifolds

In this short note, we give examples of binding sums of contact 3-manifolds that do not preserve properties such as tightness or symplectic fillability. We also prove vanishing of the Heegaard Floer contact invariant for an infinite family of binding sums where the summands are Stein fillable. This recovers a result of Wendl and Latschev-Wendl. Along the way, we rectify a subtle computational error in a paper of Juhasz-Kang concerning the spectral order of a neighbourhood of a Giroux torsion domain.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Geometric Topology

自引率

0.00%

发文量