Related papers: On PM-monoids and braid PM-monoids

In this paper, we introduce PM-mapping class monoids. Braid groups and mapping class groups have many features in common. Similarly to the notion of braid PM-monoid, PM-mapping class monoid is defined. This construction is an analogy of…

We introduce a ramified monoid, attached to each Brauer--type monoid, that is, to the symmetric group, to the Jones and Brauer monoids among others. Ramified monoids correspond to a class of tied monoids which arise from knot theory and are…

In this paper we define a monoid of pseudo braids and prove that this monoid is isomorphic to a singular braid monoid. We also prove an analogue of Markov's theorem for pseudo braids.

Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in…

We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids…

Ramified monoids are a class of monoids introduced by the authors. The main motivation for considering these monoids comes from knot theory, see [3, 4, 5]. Thus, in [2] we have studied the ramified monoids of the symmeytric group and of the…

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands,…

We construct a quasi-Garside monoid structure for the free group. This monoid should be thought of as a dual braid monoid for the free group, generalising the constructions by Birman-Ko-Lee and by the author of new Garside monoids for Artin…

We introduce the notion of a braiding on a skew monoidal category, whose curious feature is that the defining isomorphisms involve three objects rather than two. These braidings are shown to arise from, and classify, cobraidings (also known…

Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to…

Motivated by the recently introduced concept of a pseudosymmetric braided monoidal category, we define the pseudosymmetric group PS_n, as the quotient of the braid group B_n by the relations \sigma_i\sigma_{i+1}^{-1}\sigma_i=\sigma…

In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions.…

We give a solution to the word problem for the singular braid monoid SB_n. The complexity of the algorithm is quadratic in the product of the word length and the number of the singular generators in the word. Furthermore we algebraically…

In this expository paper, we discuss and compare the notions of braided and coboundary monoidal categories. Coboundary monoidal categories are analogues of braided monoidal categories in which the role of the braid group is replaced by the…

We begin with a brief sketch of what is known and conjectured concerning braided monoidal 2-categories and their applications to 4d topological quantum field theories and 2-tangles (surfaces embedded in 4-dimensional space). Then we give…

Let $(\mathrm{U},\mathrm{U}^\imath)$ be the quantum symmetric pair of arbitrary finite type and $G^*$ be the associated dual Poisson-Lie group. Generalizing the work of De Concini and Procesi, the first author introduced an integral form…

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…

We give an alternative presentation of braided monoidal categories. Instead of the usual associativity and braiding we have just one constraint (the b-structure). In the unital case, the coherence conditions for a b-structure are shown to…

We give presentations, in terms of generators and relations, for the monoids of singular braids on closed surfaces. The proof of the validity of these presentations can also be applied to verify, in a new way, the presentations given by…

We define a monoid structure on the set of $k$-equal arrangements and use this structure to define limits of braid arrangements. We compute the cohomology of the associated limits of rational models of the arrangements complex complements.…