TY - JOUR

T1 - Quantum Invariants of Knotoids

AU - Gügümcü, Neslihan

AU - Kauffman, Louis H.

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2021/11

Y1 - 2021/11

N2 - In this paper, we construct quantum invariants for knotoid diagrams in R2. The diagrams are arranged with respect to a given direction in the plane (Morse knotoids). A Morse knotoid diagram can be decomposed into basic elementary diagrams each of which is associated to a matrix that yields solutions of the quantum Yang–Baxter equation. We recover the bracket polynomial, and define the rotational bracket polynomial, the binary bracket polynomial, the Alexander polynomial, the generalized Alexander polynomial and an infinity of specializations of the Homflypt polynomial for Morse knotoids via quantum state sum models.

AB - In this paper, we construct quantum invariants for knotoid diagrams in R2. The diagrams are arranged with respect to a given direction in the plane (Morse knotoids). A Morse knotoid diagram can be decomposed into basic elementary diagrams each of which is associated to a matrix that yields solutions of the quantum Yang–Baxter equation. We recover the bracket polynomial, and define the rotational bracket polynomial, the binary bracket polynomial, the Alexander polynomial, the generalized Alexander polynomial and an infinity of specializations of the Homflypt polynomial for Morse knotoids via quantum state sum models.

UR - http://www.scopus.com/inward/record.url?scp=85114260429&partnerID=8YFLogxK

U2 - 10.1007/s00220-021-04081-3

DO - 10.1007/s00220-021-04081-3

M3 - Article

AN - SCOPUS:85114260429

VL - 387

SP - 1681

EP - 1728

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -