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The Geometry and Physics of Knots
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  • Cited by 109
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Murakami, Hitoshi and Yokota, Yoshiyuki 2018. Volume Conjecture for Knots. Vol. 30, Issue. , p. 93.

    Pavlyuk, A. M. 2018. Generalized Equidistant Chebyshev Polynomials and Alexander Knot Invariants. Ukrainian Journal of Physics, Vol. 63, Issue. 6, p. 488.

    Cho, Y. M. Oh, Seung Hun and Zhang, Pengming 2018. Knots in physics. International Journal of Modern Physics A, Vol. 33, Issue. 07, p. 1830006.

    Kauffman, Louis H. and Lomonaco, Samuel J. 2018. Braiding, Majorana fermions, Fibonacci particles and topological quantum computing. Quantum Information Processing, Vol. 17, Issue. 8,

    Anokhina, A. and Morozov, A. 2018. Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?. Journal of High Energy Physics, Vol. 2018, Issue. 4,

    Awata, Hidetoshi Kanno, Hiroaki Mironov, Andrei Morozov, Alexei and Morozov, Andrey 2018. Nontorus link from topological vertex. Physical Review D, Vol. 98, Issue. 4,

    Fehér, László Stipsicz, András and Szenthe, János 2017. Raoul Bott: Collected Papers. p. 163.

    Lawton, Sean and Sikora, Adam S. 2017. Varieties of Characters. Algebras and Representation Theory, Vol. 20, Issue. 5, p. 1133.

    Dimofte, Tudor 2017. Perturbative and nonperturbative aspects of complex Chern–Simons theory. Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue. 44, p. 443009.

    Marzuoli, Annalisa and Rasetti, Mario 2017. Spin Network Quantum Circuits. International Journal of Circuit Theory and Applications, Vol. 45, Issue. 7, p. 951.

    Sutcliffe, Paul 2017. Skyrmion Knots in Frustrated Magnets. Physical Review Letters, Vol. 118, Issue. 24,

    Rañada, Antonio F. Tiemblo, Alfredo and Trueba, José L. 2017. Time evolving potentials for electromagnetic knots. International Journal of Geometric Methods in Modern Physics, Vol. 14, Issue. 05, p. 1750073.

    Carfora, Mauro and Marzuoli, Annalisa 2017. Quantum Triangulations. Vol. 942, Issue. , p. 263.

    Dalakov, Peter 2017. Lectures on Higgs moduli and abelianisation. Journal of Geometry and Physics, Vol. 118, Issue. , p. 94.

    Ibort, Alberto and Spivak, Amelia 2017. Covariant Hamiltonian field theories on manifolds with boundary: Yang-Mills theories. Journal of Geometric Mechanics, Vol. 9, Issue. 1, p. 47.

    Morozov, A. Yu. Morozov, A. A. and Popolitov, A. V. 2017. Matrix model and dimensions at hypercube vertices. Theoretical and Mathematical Physics, Vol. 192, Issue. 1, p. 1039.

    Морозов, Алексей Юрьевич Morozov, Aleksei Yur'evich Морозов, Андрей Алексеевич Morozov, Andrei Alekseevich Пополитов, Александр Викторович and Popolitov, Aleksandr Viktorovich 2017. Матричные модели и размерности в вершинах гиперкубов. Теоретическая и математическая физика, Vol. 192, Issue. 1, p. 115.

    Морозов, Алексей Юрьевич and Morozov, Aleksei Yur'evich 2016. Существуют ли $p$-адические инварианты узлов?. Теоретическая и математическая физика, Vol. 187, Issue. 1, p. 3.

    Morozov, A. Yu. 2016. Are there p-adic knot invariants?. Theoretical and Mathematical Physics, Vol. 187, Issue. 1, p. 447.

    Adhikari, Mahima Ranjan 2016. Basic Algebraic Topology and its Applications. p. 445.


Book description

These notes arise from lectures presented in Florence under the auspices of the Accadamia dei Lincee and deal with an area that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah here presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.


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