Algebraic Structures in Knot Theory

Carmen Caprau, J. Scott Carter, Neslihan Gugumcu , Sam Nelsen

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English

American Mathematical Society
15 November 2025

Geometry; Topology

Series: Contemporary Mathematics

This volume contains the proceedings of the AMS Western Sectional Meeting on Algebraic Structures in Knot Theory held on May 6-7, 2023, at California State University, Fresno, California.

Modern knot theory includes the study of a diversity of different knotted objects-classical knots, surface-links, knotoids, spatial graphs, and more. Knot invariants are tools for probing the structure of these generalized knots. Many of the most effective knot invariants take the form of algebraic structures. In this volume we collect some recent work on algebraic structures in knot theory, including topics such as braid groups, skein algebras, Gram determinants, and categorifications such as Khovanov homology.

Edited by: Carmen Caprau, J. Scott Carter, Neslihan Gugumcu, Sam Nelsen
Imprint: American Mathematical Society
Country of Publication: United States
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9781470475581
ISBN 10: 1470475588
Series: Contemporary Mathematics
Pages: 234
Publication Date: 15 November 2025
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Forthcoming

Articles Rostislav Akhmechet and Melissa Zhang, On equivariant Khovanov homology Christine Ruey Shan Lee, Computing Khovanov homology via categorified Jones-Wenzl projectors Ioannis Diamantis, A survey on skein modules via braids Blake Mellor and Robin Wilson, Topological symmetries of the Heawood family Tonie Scroggin, On the cohomology of two stranded braid varieties Kate Kearney, Symmetry of three component links Paolo Cavicchioli and Sofia Lambropoulou, The mixed Hilden braid group and the plat equivalence in handlebodies Jason Joseph and Puttipong Pongtanapaisan, Meridional rank, welded knots, and bridge trisections Audrey Baumheckel, Carmen Caprau and Conor Righetti, On an invariant for colored classical and singular links Dionne Ibarra and Gabriel Montoya-Vega, A study of Gram determinants in knot theory

Carmen Caprau, California State University, Fresno, California. J. Scott Carter, University of South Alabama, Mobile, Alabama. Neslihan Gugumcu, Izmir Institute of Technology, Turkey. Sam Nelsen, Claremont McKenna College, California.