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On a canonical lift of Artin's representation to loop braid groups
Celeste Damiani, João Faria Martins, Paul Purdon Martin
Each pointed topological space has an associated -module, obtained from action of its first homotopy group on its second homotopy group. For the -ball with a trivial link wit…
On the group of ring motions of an H-trivial link
Celeste Damiani, Seiichi Kamada
In this paper we compute a presentation for the group of ring motions of the split union of a Hopf link with Euclidean components and a Euclidean circle. A key part of this work is…
Towards a version of Markov's theorem for ribbon torus-links in
Celeste Damiani
In classical knot theory, Markov's theorem gives a way of describing all braids with isotopic closures as links in . We present a version of Markov's theorem for exte…
A Markov's theorem for extended welded braids and links
Celeste Damiani
Extended welded links are a generalization of Fenn, Rimányi, and Rourke's welded links. Their braided counterpart are extended welded braids, which are closely related to ribbon br…
Unrestricted virtual braids, fused links and other quotients of virtual braid groups
Valeriy Bardakov, Paolo Bellingeri, Celeste Damiani
We consider the group of unrestricted virtual braids, describe its structure and explore its relations with fused links. Also, we define the groups of flat virtual braids and virtu…
Alexander invariants of ribbon tangles and planar algebras
Celeste Damiani, Vincent Florens
Ribbon tangles are proper embeddings of tori and cylinders in the -ball~, "bounding" -manifolds with only ribbon disks as singularities. We construct an Alexander invari…