| Title | Octahedral developing of knot complement II: Ptolemy coordinates and applications |
| Author | |
| Corresponding Author | Kim, Seonhwa |
| Publication Years | 2023-08-01
|
| DOI | |
| Source Title | |
| ISSN | 0218-2165
|
| EISSN | 1793-6527
|
| Volume | 32Issue:09 |
| Abstract | 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. |
| Keywords | |
| URL | [Source Record] |
| Indexed By | |
| Language | English
|
| SUSTech Authorship | Others
|
| Funding Project | 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 Research Area | Mathematics
|
| WOS Subject | Mathematics
|
| WOS Accession No | WOS:001066573100003
|
| Publisher | |
| ESI Research Field | MATHEMATICS
|
| Data Source | Web of Science
|
| Citation statistics |
Cited Times [WOS]:0
|
| Document Type | Journal Article |
| Identifier | http://kc.sustech.edu.cn/handle/2SGJ60CL/575818 |
| Department | Southern University of Science and Technology |
| Affiliation | 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 |
| Recommended Citation 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).
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