Virtual Knots and Projective Knot Homology

DOI

10.2991/978-94-6463-789-2_8How to use a DOI?

Keywords

Kauffman bracket polynomial; Khovanov homology; Rasmussen invariant; Projective space; Affine knots; Virtual knots and Flype move

Abstract

The article describes a construction of a knot homology theory for knots in RP³. This is achieved by defining a map from projective knots to virtual knots and importing the virtual Khovanov theory through this map. Structural features of knots in RP³ is analyzed in detail for the construction of the map. The article can be seen as an introduction to non-classical knot theory through the example of projective knots.

Copyright

© 2025 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Visakh Narayanan
PY  - 2025
DA  - 2025/07/17
TI  - Virtual Knots and Projective Knot Homology
BT  - Proceedings of the International Conference on Knots, Quivers and Beyond (ICKQB 2025)
PB  - Atlantis Press
SP  - 89
EP  - 104
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-789-2_8
DO  - 10.2991/978-94-6463-789-2_8
ID  - Narayanan2025
ER  -