arXiv  & Pure

Knots and braids in 3-manifolds

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Current Research/Projects

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1. Knot Theory of Lens Spaces, (with S.Lambropoulou, B. Gabrovsek & A. Cattabriga),  book for Walter De Gruyter Publishers - manuscript in preparation.
2. A new invariant of doubly periodic tangles, (with Sonia Mahmoudi and Sofia Lambropoulou) - manuscript in preparation. 
3. Topological bonded knots and knotoids, (with L. Kauffman & S. Lambropoulou) - manuscript in preparation.
4. On Probabilistic Knots (with L. Kauffman & S. Lambropoulou).
5. Knots in Biology (with S. Lambropoulou) - manuscript in preparation.
6. Periodic Structures (with S. Lambropoulou & S. Mahmoudi).
7. The HOMFLYPT skein module of S^1xS^2 via the generalized Hecke algebra of type B.
8. Tied links, pseudo links & tied pseudo links in 3-manifolds.
9. Quantum Economics, initial stage.

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Submitted for Publication

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     1. I. D., S. Lambropoulou, S. Mahmoudi, Directional Invariants of Doubly Periodic

        Tangles, arXiv[GT] 2404.05092 (2024).

     2. I. D., S. Lambropoulou, S. Mahmoudi, Equivalence of Doubly Periodic Tangles, 

        arXiv[GT] 2310.00822 (2023).    

     3. I. Diamantis, The Kauffman bracket skein module of S^1 x S^2 via braids, arXiv[GT]

        2307.12275 (2023).

     4. I. Diamantis, A survey on skein modules via braids, arXiv[GT] 2311.06556 (2023).

Published

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1. I. Diamantis, The Kauffman bracket skein module of the lens spaces via unoriented braids, Communications in Contemporary Mathematics, Vo,26, No.2, 2250076, 2024. https://doi.org/10.1142/S0219199722500766.
2. I. Diamantis, The Kauffman bracket skein module of the complement of (2, 2p+1)-torus knots via braids, Topology and its Applications, Volume 327, 15 March 2023, 108433. https://doi.org/10.1016/j.topol.2023.108433.
3. I. Diamantis, Pseudo links and singular links in the Solid Torus, Communications in Mathematics, Volume 31 (2023), Issue 1, https://doi.org/10.46298/cm.10438.
4. I. Diamantis, Knotoids, pseudo knotoids, Braidoids and pseudo braidoids on the Torus, Commun. Korean Math. Soc. 2022; 37(4): 1221-1248, https://doi.org/10.4134/CKMS.c210169
5. I. Diamantis, Pseudo links in handlebodies, Bulletin of the Hellenic Mathematical Society Vol.65, 2021, p.1 7-34.
6. I. Diamantis, Tied links in various topological settings, Journal of Knot theory and its Ramifications, Vol. 30, No. 07, 2150046 (2021), doi: 10.1142/S0218216521500462.
7. I. Diamantis, Tied pseudo links & Pseudo knotoids, Mediterranean Journal of Mathematics, (2021) 18:201, doi: 10.1007/s00009-021-01842-1.
8. I. Diamantis, HOMFLYPT skein sub-modules of the lens spaces L(p, 1), Topology and its Applications (2021), Volume 301, 1 September 2021, 107500, https://doi.org/10.1016/j.topol.2020.107500.
9. I. Diamantis, The Kauffman bracket skein module of the handlebody of genus 2 via braids, Journal of Knot Theory and its Ramifications Vol. 28, No. 13, 1940020 (2019), DOI: 10.1142/S0218216519400200.
10. I. Diamantis, S. Lambropoulou, An important step for the computation of the HOMFLYPT skein module of the lens spaces L(p,1) via braids, Journal of Knot Theory and its Ramifications 28, No.11, 2019,  DOI: 10.1142/S0218216519400078.
11. I. Diamantis, An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids, (2019) In: Adams C. et al. (eds) Knots, Low-Dimensional Topology and Applications. KNOTS16 2016. Springer Proceedings in Mathematics & Statistics, vol 284. Springer, Cham. Check out the book here!
12. I. Diamantis, S. Lambropoulou, The braid approach to the Homflypt skein module of the lens spaces L(p,1), in "Algebraic Modeling of Topological and Computational Structures and Applications", Springer Proceedings in Mathematics & Statistics (PROMS), S. Lambropoulou, P. Stefaneas, D. Theodorou, L. Kauffman (Eds) (2017).          Check out the book here!
13. I. Diamantis, S. Lambropoulou, J. Przytycki, Topological steps toward the HOMFLYPT skein module of the lens spaces L(p,1) via braids, J. Knot Theory Ramifications 25, No. 14 (2016).
14. I. Diamantis, S. Lambropoulou, A new basis for the Homflypt skein module of the solid torus, Journal of Pure and Applied Algebra (2016) pp. 269-295.
15. I. Diamantis, S. Lambropoulou, Braid equivalences in 3-manifolds with rational surgery description, Topology and its Applications 194 (2015) pp. 269-295.
16. S. Lambropoulou, S. Antoniou, N. Samardzija, I. Diamantis, Topological Surgery and Dynamics, Mathematisches Forschunginstitut Oberwolfach, Report No.26/2014 (Workshop: Algebraic Structures in Low-Dimensional Topology).
17. S. Lambropoulou, I. Diamantis, D. Kodokostas, The algebraic approach toward the Homflypt skein modules of c.c.o. 3-manifolds described by the unknot or the 2-unlink, AMS Preliminary Report, 2015.

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Monographs

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1. I. Diamantis, B. Gabrovsek, M. Mrockowski, S. Lambropoulou, "Knot theory of lens spaces", Walter De Gruyter Publishers [2024].
2. I. Diamantis, "Sequences and Series", Central West Publishers Australia [February 2019]. Check it out here: GoogleBooks and order here: BooksAMillion, Amazon.com.
   

Theses

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PhD Thesis (in English)

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MSc Thesis (in Greek)

Research Interests & More

# Skein modules of 3-manifolds, 3-manifold invariants, Quantum invariants.

# Knot Algebras & Braid groups, Iwahori-Hecke algebras, Temperley-Lieb algebras.

# Pseudo links, Singular links, Tied links & Tied pseudo links in 3-manifolds.

# Knotoids, Braidoids and applications, Pseudo and tied knotoids.

# Applications of Knot theory to Chemistry, DNA-topology, Economics, Physics &

    Graphs.

# (Doubly) Periodic Structures, Weaves, Tilings.

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Citations: 259 Google Scholar &    127 Scopus & 298 ResearchGate & 130 Pure

h-index:      10 Google Scholar &        7 Scopus &      9 ResearchGate

i10-index:   10 Google Scholar 

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