MPS-Ascend: Bi-Orderability, Fibered Knots, and Cyclic Branched Covers

MPS-Ascend：双向可排序性、纤维结和循环分支覆盖层

• 批准号: 2213213
• 负责人: Jonathan Johnson
• 金额: $ 17.25万
• 依托单位: Johnson, Jonathan C
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2213213&HistoricalAwards=false
• 关键词: MPS; Ascend; Bi; Orderability; Fibered

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Jonathan Johnson is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research and activities related to broaden participation by groups underrepresented in STEM. This fellowship to Dr. Johnson supports the research project entitled "MPS-Ascend: Bi-Orderability, Fibered Knots, and Cyclic Branched Covers", under the mentorship of a sponsoring scientist. The host institution for the fellowship is Oklahoma State University, and the sponsoring scientist is Dr. Neil Hoffman. Motivated by the PI’s past research, this project includes a novel conjecture linking bi-orderability of fibered and two-bridge knot groups to the L-space conjecture conditions of the cyclic branched covers of the knots, a possible characterization of bi-orderability in terms of the Alexander polynomial of knots, and new methods of producing examples of bi-orderable 3-manifold groups. For broadening participation, the PI plans to create a Directed Reading Program at Oklahoma State University, with a focus on recruiting students from underrepresented groups, particularly the university's large Native American population. An additional contribution will be to create publicly accessible online videos covering a broad range of topics in low-dimensional topology, aimed at undergraduate students and early career mathematiciansThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项全部或部分由《2021 年美国救援计划法案》（公法 117-2）资助，PI Jonathan Johnson 被授予美国国家科学基金会数学和物理科学提升博士后研究奖学金 (NSF MPS-Ascend)，以开展这项研究。一项与扩大 STEM 中代表性不足的群体的参与相关的研究和活动计划。约翰逊博士的这项奖学金支持题为“MPS-Ascend：Bi-Orderability，Fibered”的研究项目。结和循环分支覆盖物”，在赞助科学家的指导下。该奖学金的主办机构是俄克拉荷马州立大学，赞助科学家是尼尔·霍夫曼博士。受 PI 过去研究的启发，该项目包括一个新颖的猜想将纤维结和双桥结群的双有序性与结的循环分支覆盖的 L 空间猜想条件联系起来，这是根据亚历山大的双有序性的可能表征为了扩大参与范围，PI 计划在俄克拉荷马州立大学创建一个定向阅读项目，重点是从代表性不足的群体中招募学生，特别是该大学的学生。另一项贡献是针对本科生和早期职业数学家制作涵盖低维拓扑广泛主题的公开在线视频。该奖项反映了 NSF 的法定使命，并被视为值得通过使用基金会的智力优点和更广泛的影响审查标准进行评估来支持。

项目成果

Residual torsion-free nilpotence, biorderability and pretzel knots

残余无扭幂零性、生物有序性和椒盐结

• DOI: 10.2140/agt.2023.23.1787
• 发表时间: 2023-01
• 期刊: Algebraic & Geometric Topology
• 作者: Johnson; Jonathan
• 通讯作者: Jonathan

Residual torsion-free nilpotence, bi-orderability, and two-bridge links

残余无扭零力、双向有序性和双桥连杆

• DOI: 10.4153/s0008414x2300007x
• 发表时间: 2023-01
• 期刊: Canadian Journal of Mathematics
• 作者: Johnson; Jonathan
• 通讯作者: Jonathan