Stable homotopy refinement of Seiberg-Witten theory in low-dimensional topology

低维拓扑中Seiberg-Witten理论的稳定同伦细化

• 批准号: 18K13419
• 负责人: KHANDHAWIT TIRAS
• 金额: $ 0.83万
• 依托单位: Okinawa Institute of Science and Technology Graduate University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Early-Career Scientists
• 财政年份: 2018
• 资助国家: 日本
• 起止时间: 2018-04-01 至 2020-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18K13419/
• 关键词: Seiberg-Witten theory; Low-dimensional topology; Stable homotopy theory; 低次元トポロジー; ゲージ理論; Seiberg-Witten Theory; Stable homotopy

One of the major research achievements is rigorous construction of relative Bauer-Furuta invariants and proof of the gluing theorem. The theorem generalizes to larger classes of manifolds. There are some direct application to compute Bauer-Furuta invariant of a 4-manifold after doing surgery as well as to find a condition for having embedded 2-sphere in term of Bauer-Furuta invariant.

主要的研究成就之一是严格构造相对的鲍尔 - 毛状不变式和粘合定理的证明。定理概括为较大的歧管类。在进行手术后，有一些直接应用来计算4个manifold的Bauer-furuta不变性，并找到了在Bauer-furuta不变的术语中嵌入2次球的条件。

项目成果

Gluing theorems for Bauer-Furuta invariants

Bauer-Furuta 不变量的粘合定理

• 发表时间: 2018
• 作者: Jin Takahashi;Hikaru Yamamoto;桑垣樹;田神慶士;阿部拓;蓮井翔;古賀勇;Ryomei Iwasa and Wataru Kai;Hikaru Yamamoto;桑垣樹;阿部拓;Ade Irma Suriajaya;田神慶士;Wataru Kai;阿部拓;Sho Hasui;Ade Irma Suriajaya;Sho Hasui;田神慶士;山本光;古賀勇;Hiraku Abe;Ade Irma Suriajaya;Ryomei Iwasa and Wataru Kai;Isami Koga;桑垣樹;阿部拓;山本光;古賀勇;Ade Irma Suriajaya;Wataru Kai;古賀勇;Hiraku Abe;桑垣樹;山本光;Takao Yamazaki;Ade Irma Suriajaya;桑垣樹;古賀勇;甲斐亘;Hiraku Abe;Ade Irma Suriajaya;Hiraku Abe;桑垣樹;甲斐亘;山本光;Ade Irma Suriajaya;Ade Irma Suriajaya;Hiraku Abe;Tirasan Khandhawit;桑垣樹;甲斐亘;Hikaru Yamamoto;Ade Irma Suriajaya;Hiraku Abe;Tirasan Khandhawit;阿部拓;桑垣樹;Ade Irma Suriajaya;Hikaru Yamamoto;Ade Irma Suriajaya;Hiraku Abe;Hikaru Yamamoto;桑垣樹;Tirasan Khandhawit
• 通讯作者: Tirasan Khandhawit

A relative family version of the Bauer-Furuta invariant

Bauer-Furuta 不变量的相对家庭版本

• 发表时间: 2019
• 作者: Jin Takahashi;Hikaru Yamamoto;桑垣樹;田神慶士;阿部拓;蓮井翔;古賀勇;Ryomei Iwasa and Wataru Kai;Hikaru Yamamoto;桑垣樹;阿部拓;Ade Irma Suriajaya;田神慶士;Wataru Kai;阿部拓;Sho Hasui;Ade Irma Suriajaya;Sho Hasui;田神慶士;山本光;古賀勇;Hiraku Abe;Ade Irma Suriajaya;Ryomei Iwasa and Wataru Kai;Isami Koga;桑垣樹;阿部拓;山本光;古賀勇;Ade Irma Suriajaya;Wataru Kai;古賀勇;Hiraku Abe;桑垣樹;山本光;Takao Yamazaki;Ade Irma Suriajaya;桑垣樹;古賀勇;甲斐亘;Hiraku Abe;Ade Irma Suriajaya;Hiraku Abe;桑垣樹;甲斐亘;山本光;Ade Irma Suriajaya;Ade Irma Suriajaya;Hiraku Abe;Tirasan Khandhawit
• 通讯作者: Tirasan Khandhawit