Möbius strip diagram algebras
Diagram algebras in a nonorientable world: strands can carry handles and Möbius strip features.
Data
- Title: Möbius strip diagram algebras
- Authors: Daniel W. Collison and Daniel Tubbenhauer
- Status: preprint. Last update: Thu, 12 Feb 2026 05:17:51 UTC
- arXiv: https://arxiv.org/abs/2602.11591
Abstract
We introduce Möbius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and Möbius strip features. We identify the resulting diagram category with a linear quotient of a nonorientable two-dimensional cobordism category. Finally, we develop the associated cell theory and use it to classify the simple modules and compute dimensions in a range of cases.
What is the point?
Classical diagram algebras usually live in orientable two-dimensional worlds. This paper changes the surface: nonorientable features enter the diagram calculus, producing new algebras and new cell theory while keeping the pictures concrete.
nonorientable cobordisms.
handles and Möbius features.
cells, simples and dimensions.
Pictures
The Möbius relation and the local feature it encodes.
