南方科技大学知识苑(SUSTech KC): Octahedral developing of knot complement II: Ptolemy coordinates and applications

题名	Octahedral developing of knot complement II: Ptolemy coordinates and applications
作者	Kim, Hyuk 1; Kim, Seonhwa 2; Yoon, Seokbeom3
通讯作者	Kim, Seonhwa
发表日期	2023-08-01
DOI	10.1142/S0218216523500578
发表期刊	JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 影响因子和分区
ISSN	0218-2165
EISSN	1793-6527
卷号	32 期号:09
摘要	It is known that a knot complement (minus two points) decomposes into ideal octahedra with respect to a given knot diagram. In this paper, we study the Ptolemy variety for such an octahedral decomposition in perspective of Thurston's gluing equation variety. More precisely, we compute explicit Ptolemy coordinates in terms of segment and region variables, the coordinates of the gluing equation variety motivated from the volume conjecture. As a consequence, we present an explicit formula for computing the obstruction to lifting a boundary-parabolic PSL(2, DOUBLE-STRUCK CAPITAL C)-representation to boundary-unipotent SL(2, DOUBLE-STRUCK CAPITAL C)-representation. We also present a diagrammatic algorithm to compute a holonomy representation of the knot group.
关键词	Knots diagrams octahedral decompositions Ptolemy coordinates
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	其他
资助项目	National Research Foundation (NRF) of Korea - Ministry of Education[NRF-2018R1A2B6005691] ; NRF of Korea - Ministry of Education[2022R1I1A1A01063774] ; Institute for Basic Science[IBS-R003-D1]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:001066573100003
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
ESI学科分类	MATHEMATICS
来源库	Web of Science
引用统计	被引频次[WOS]：0
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/575818
专题	南方科技大学
作者单位	1.Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea 2.Univ Seoul, Dept Math, Seoul 02504, South Korea 3.Southern Univ Sci & Technol, Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China
推荐引用方式 GB/T 7714	Kim, Hyuk,Kim, Seonhwa,Yoon, Seokbeom. Octahedral developing of knot complement II: Ptolemy coordinates and applications[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS,2023,32(09).
APA	Kim, Hyuk,Kim, Seonhwa,&Yoon, Seokbeom.(2023).Octahedral developing of knot complement II: Ptolemy coordinates and applications.JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS,32(09).
MLA	Kim, Hyuk,et al."Octahedral developing of knot complement II: Ptolemy coordinates and applications".JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 32.09(2023).