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

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），以开展一项与扩大STEM中代表性不足群体参与相关的研究和活动计划。约翰逊博士的研究项目名为“MPS-Ascend：双序性、纤维结和循环分支盖”，由一位赞助科学家指导。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。在PI过去研究的启发下，本项目包括将纤维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的一个新猜想，用结的Alexander多项式对双有序性的可能表征，以及产生双有序3流形群的新方法。为了扩大参与，PI计划在俄克拉荷马州立大学（Oklahoma State University）创建一个定向阅读项目（Directed Reading Program），重点从代表性不足的群体中招募学生，尤其是该校人数众多的印第安人群体。另一项贡献将是创建可公开访问的在线视频，涵盖低维拓扑的广泛主题，目标是本科生和早期职业数学家。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.