20.500.12556/RUP-22057 Passing from plat closure to standard closure of braids in R^3, in handlebodies and in thickened surfaces Prehod od ploskovnega zapiranja do standardnega zapiranja pletenic v R^3, v ročajnih telesih in v odebeljenih ploskvah Given a knot or link in the form of plat closure of a braid, we describe an algorithm to obtain a braid representing the same knot or link with the standard closure, and vice-versa. We analyze the three cases of knots and links in ℝ^3, in handlebodies and in thickened surfaces, and we give for each one a detailed construction of the relative algorithm, with proofs of the results and the calculation of the computational complexity. Indeed, we show that the algorithm has quadratic computational complexity in the number of crossings and loop generators of the braid when passing from plat to standard closure, while it has linear computational complexity in the number of crossings generators of the braid when passing from standard to plat closure. The article includes numerous illustrations to facilitate the understanding of the results, as well as an example of implementation of the algorithm for the general case. standard closure of braids plat closure of braids classical knots and links knots and links in the handlebody knots and links in thickened surfaces algorithms and complexity standardno zapiranje pletenic ploskovno zapiranje pletenic klasični vozli in povezave vozli in povezave v ročajnem telesu vozli in povezave v odebeljenih ploskvah algoritmi in zahtevnost true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-11-03 09:41:30 2025-11-03 09:41:31 2025-12-21 21:56:50 0000-00-00 00:00:00 2025 0 0 37 str. no. 4, [article no.] P4.10 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-11-03 51 1855-3974 10.26493/1855-3974.3317.25b AMC_Cavicchioli,_Lambropoulou_2025.pdf AMC_Cavicchioli,_Lambropoulou_2025.pdf 1 97F48A321E3414C4FDCEA8F89A7A2871 70a7f5617c2969dd026e01ff3533579c45865d2cc28bdfd75950e5a0cfd959af be8ea547-b891-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32002 Založba Univerze na Primorskem 0 0 0