New approach to low dimensional topology by using quandle and branched covering

2017 Fiscal Year Final Research Report

• Project/Area Number: 16K17589
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tokyo University of Agriculture and Technology
• Principal Investigator: Hatakenaka Eri 東京農工大学, 工学(系)研究科(研究院), 講師 (00532558)
• Project Period (FY): 2016-04-01 – 2018-03-31
• Keywords: 低次元トポロジー / 位相不変量 / カンドル / 分岐被覆 / 三次元多様体

Outline of Final Research Achievements

By a covering presentation of a 3-manifold, we mean a labelled link (i.e., a link with a monodromy representation), which presents the 3-manifold as the simple 4-fold covering space of the 3-sphere branched along the link with the given monodromy. It is known that wo labelled links present a homeomorphic 3-manifold if and only if they are related by a finite sequence of some local moves. This research presents a method for constructing topological invariants of 3-manifolds based on their covering presentations. The proof of the topological invariance is shown by verifying the invariance under the local moves. As an example of such invariants, we present the Dijkgraaf-Witten invariant of 3-manifolds.

Free Research Field

低次元トポロジー