Qualgebras and knotted 3-valent graphs

• Autorzy: Victoria Lebed
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to new algebraic structures, called qualgebras and squandles. Topologically, they emerge as an algebraic counterpart of knotted 3-valent graphs, just like quandles can be seen as an "algebraization" of knots. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. We discuss basic properties of these structures, and introduce and study the notions of qualgebra/squandle 2-cocycles and 2-coboundaries. Knotted 3-valent graph invariants are constructed by counting qualgebra/squandle colorings of graph diagrams, and are further enhanced using 2-cocycles. A classification of size 4 qualgebras/squandles and a description of their second cohomology groups are given.

Kategorie tematyczne

• 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
• 57M27: Invariants of knots and 3-manifolds
• 17D99: None of the above, but in this section
• 20N99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 230
• Numer: 2
• Strony: 167-204

Daty

wydano

2015

Twórcy

autor

Victoria Lebed

• OCAMI, Osaka City University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka, 558-8585, Japan

Identyfikatory

DOI

10.4064/fm230-2-3