Framization and Deframization
Francesca Aicardi, Jes\'us Juyumaya, Paolo Papi

TL;DR
This paper introduces the concepts of framization and deframization for braid-related monoids and algebras, providing a geometric foundation and detailed procedures, with implications for knot theory.
Contribution
It defines and studies framization and deframization of several monoids and algebras, expanding the algebraic framework related to knot theory.
Findings
Defined framization and deframization procedures
Applied these procedures to specific monoids and algebras
Provided detailed examples and geometric interpretations
Abstract
Starting from the geometric construction of the framed braid group, we define and study the framization of several Brauer-type monoids and also the set partition monoid, all of which appear in knot theory. We introduce the concept of deframization, which is a procedure to obtain a tied monoid from a given framed monoid. Furthermore, we show in detail how this procedure works on the monoids mentioned above. We also discuss the framization and deframization of some algebras, which are deformations, respectively, of the framized and deframized monoids discussed here.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
