☆ 4.5 Article

Representations of Flat Virtual Braids by Automorphisms of Free Group

SYMMETRY-BASEL (2023)

Related references

Note: Only part of the references are listed.

Article Mathematics

Virtual Artin groups

Paolo Bellingeri et al.

Summary: Starting from the observation of the mixed standard presentations in a virtual braid group, this paper defines a virtual Artin group that combines the standard presentation of the Artin group with the Coxeter group and some mixed relations. The paper also calculates presentations for the subgroups and proves the triviality of the center of any virtual Artin group. Furthermore, it explores the properties of KVA[Gamma] and VA[Gamma] in specific cases.

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY (2023)

Add to Collection

Article Multidisciplinary Sciences

Recurrent Generalization of F-Polynomials for Virtual Knots and Links

Amrendra Gill et al.

Summary: In this paper, weight functions for ordered orientable virtual and flat virtual links are introduced, providing a recursive construction for new invariants. It is demonstrated through explicit examples that the newly defined polynomial invariants are stronger than F-polynomials.

SYMMETRY-BASEL (2022)

Add to Collection

Article Multidisciplinary Sciences

Invariants of Bonded Knotoids and Applications to Protein Folding

Neslihan Gugumcu et al.

Summary: This paper studies bonded knotoids with extra graphical structure in the settings of rigid vertex and topological vertex graphs. The authors construct bonded knotoid invariants by applying tangle insertion and unplugging at bonding sites. They demonstrate that these invariants can be used for the analysis of the topological structure of proteins.

SYMMETRY-BASEL (2022)

Add to Collection

Article Mathematics

An unknotting invariant for welded knots

A. Gill et al.

Summary: In this study, we analyze a local twist move on welded knots analogous to the virtualization move on virtual knots. By defining an invariant called unknotting twist number and establishing a lower bound on the twist number using Alexander quandle coloring, we relate the unknotting twist number to warping degree and welded unknotting number. Additionally, we investigate the Gordian distance between welded knots by twist move and define the corresponding Gordian complex.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES (2021)

Add to Collection

Article Mathematics

Gordian complexes of knots and virtual knots given by region crossing changes and arc shift moves

Amrendra Gill et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2020)

Add to Collection

Article Mathematics, Applied

An unknotting index for virtual links

K. Kaur et al.

TOPOLOGY AND ITS APPLICATIONS (2019)

Add to Collection

Article Mathematics

Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants

Kirandeep Kaur et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2018)

Add to Collection

Article Mathematics

Representations of virtual braids by automorphisms and virtual knot groups

Valeriy G. Bardakov et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2017)

Add to Collection

Article Mathematics

Generalizations of the Wada representations and virtual link groups

Yu. A. Mikhalchishina

SIBERIAN MATHEMATICAL JOURNAL (2017)

Add to Collection

Article Multidisciplinary Sciences

Proteins analysed as virtual knots

Keith Alexander et al.

SCIENTIFIC REPORTS (2017)

Add to Collection

Article Mathematics

A zero polynomial of virtual knots

Myeong-Ju Jeong

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2016)

Add to Collection

Article Mathematics

Unrestricted virtual braids, fused links and other quotients of virtual braid groups

Valeriy G. Bardakov et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2015)

Add to Collection

Article Mathematics

Alexander invariants for virtual knots

Hans U. Boden et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2015)

Add to Collection

Article Mathematics

ACTIONS OF THE N-STRAND BRAID GROUPS ON THE FREE GROUP OF RANK N WHICH ARE SIMILAR TO THE ARTIN REPRESENTATION

Tetsuya Ito

QUARTERLY JOURNAL OF MATHEMATICS (2015)

Add to Collection

Article Mathematics

A LINKING NUMBER DEFINITION OF THE AFFINE INDEX POLYNOMIAL AND APPLICATIONS

Lena C. Folwaczny et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2013)

Add to Collection

Article Mathematics

A POLYNOMIAL INVARIANT OF VIRTUAL LINKS

Zhiyun Cheng et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2013)

Add to Collection

Article Mathematics

AN AFFINE INDEX POLYNOMIAL INVARIANT OF VIRTUAL KNOTS

Louis H. Kauffman

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2013)

Add to Collection

Article Mathematics, Applied

The classification of Wada-type representations of braid groups

Tetsuya Ito

JOURNAL OF PURE AND APPLIED ALGEBRA (2013)

Add to Collection

Article Mathematics

An index polynomial invariant for flat virtual knots

Young Ho Im et al.

EUROPEAN JOURNAL OF COMBINATORICS (2010)

Add to Collection

Article Mathematics

INDEX POLYNOMIAL INVARIANT OF VIRTUAL LINKS

Young Ho Im et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2010)

Add to Collection

Article Mathematics

AN EXTENDED BRACKET POLYNOMIAL FOR VIRTUAL KNOTS AND LINKS

Louis H. Kauffman

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2009)

Add to Collection

Article Mathematics

VIRTUAL CROSSING NUMBER AND THE ARROW POLYNOMIAL

H. A. Dye et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2009)

Add to Collection

Article Mathematics

Virtual braids

LH Kauffman et al.

FUNDAMENTA MATHEMATICAE (2004)

Add to Collection

Article Mathematics

What is a virtual link?

Greg Kuperberg

ALGEBRAIC AND GEOMETRIC TOPOLOGY (2003)

Add to Collection

Article Mathematics

Alexander groups and virtual links

DS Silver et al.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2001)

Add to Collection

Article Mathematics

Forbidden moves unknot a virtual knot

T Kanenobu

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS (2001)

Add to Collection

Article Mathematics

Finite-type invariants of classical and virtual knots

M Goussarov et al.

TOPOLOGY (2000)

Add to Collection

© Peeref 2019-2024. All rights reserved.