@phdthesis{oai:sucra.repo.nii.ac.jp:00010402,
 author = {阿部, 翠空星},
 month = {},
 note = {44 p., 1 Introduction 2
2 Preliminaries 4
2.1 Knots and their diagrams . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Quantum invariants . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Vassiliev invariants (Finite type invariants). . . . . . . . . . . . . 9
2.4 Quandle (shadow) cocycle invariants . . . . . . . . . . . . . . . . 12
2.5 Heegaard splitting . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6 Dijkgraaf-Witten invariants . . . . . . . . . . . . . . . . . . . . . 16
2.7 Lens space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 On Vassiliev invariants of degrees 2 and 3 for torus knots 17
3.1 Primitive Vassiliev invariants and torus knots . . . . . . . . . . . 18
3.2 Results of this section . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Definition of quasi finite type invariants and finite type invariants of some 3-manifolds 22
4.1 Quasi finite type invariants . . . . . . . . . . . . . . . . . . . . . 24
4.2 Finite type invariants of some 3-manifolds of double branched covering of links. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 Relations between quandle shadow cocycle invariants and finite type invariants 30
5.1 Main theorems and Proofs of quandle 2-cocycle invariants version 31
5.2 Main theorem and Proof of quandle shadow 3-cocycle invariants version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Appendix 33, 指導教員 : 下川航也, text, application/pdf},
 school = {埼玉大学},
 title = {On finite type invariants of knots and 3-manifolds},
 year = {2016},
 yomi = {アベ, スクセ}
}