Zobrazeno 1 - 10
of 108
pro vyhledávání: '"Alexis Virelizier"'
Autor:
Kursat Sozer, Alexis Virelizier
Publikováno v:
Adv.Math.
Adv.Math., 2023, 428, pp.109155. ⟨10.1016/j.aim.2023.109155⟩
Kursat Sozer
Adv.Math., 2023, 428, pp.109155. ⟨10.1016/j.aim.2023.109155⟩
Kursat Sozer
International audience; Given a crossed module $\chi$, we introduce $\chi$-graded monoidal categories and $\chi$-fusion categories. We use spherical $\chi$-fusion categories to construct (via the state sum method) 3-dimensional Homotopy Quantum Field
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0333ffc2b0a334861f55a78e0aa24162
https://hal.science/hal-03736640
https://hal.science/hal-03736640
Autor:
Vladimir Turaev, Alexis Virelizier
Publikováno v:
Int.J.Math.
Int.J.Math., 2020, 31 (10), pp.2050076. ⟨10.1142/S0129167X20500767⟩
Int.J.Math., 2020, 31 (10), pp.2050076. ⟨10.1142/S0129167X20500767⟩
Let [Formula: see text] be a discrete group and [Formula: see text] be an additive spherical [Formula: see text]-fusion category. We prove that the state sum 3-dimensional HQFT derived from [Formula: see text] is isomorphic to the surgery 3-dimension
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b32c79dc95a5d3d8b800e6dab58cc5bb
https://hal.archives-ouvertes.fr/hal-02423711
https://hal.archives-ouvertes.fr/hal-02423711
Autor:
Alexis Virelizier, Rinat Kashaev
Publikováno v:
Algebr. Geom. Topol. 19, no. 5 (2019), 2575-2624
In the 90s, based on presentations of 3-manifolds by Heegaard diagrams, Kuperberg associated a scalar invariant of 3-manifolds to each finite dimensional involutory Hopf algebra over a field. We generalize this construction to the case of involutory
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74c13064596e66ab719f632672619237
https://projecteuclid.org/euclid.agt/1572055268
https://projecteuclid.org/euclid.agt/1572055268
Autor:
Vladimir Turaev, Alexis Virelizier
This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research.Part 1 introduces monoidal categories and several
Autor:
Vladimir Turaev, Alexis Virelizier
Publikováno v:
Monoidal Categories and Topological Field Theory ISBN: 9783319498331
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c9889c1237f143744ff43a26ccb39353
https://doi.org/10.1007/978-3-319-49834-8_17
https://doi.org/10.1007/978-3-319-49834-8_17
Autor:
Vladimir Turaev, Alexis Virelizier
Publikováno v:
Monoidal Categories and Topological Field Theory ISBN: 9783319498331
We establish here several properties of the state sum graph TQFT. Two of these properties (Theorems 16.1 and 16.2) will be used in the next chapter.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2d8e40b1564e006f272059926a178435
https://doi.org/10.1007/978-3-319-49834-8_16
https://doi.org/10.1007/978-3-319-49834-8_16
Autor:
Alexis Virelizier, Vladimir Turaev
Publikováno v:
Monoidal Categories and Topological Field Theory ISBN: 9783319498331
The study of monoidal categories originated in the work of Jean Benabou [Ben] and Saunders Mac Lane [ML1]. In this chapter, we review the basics of the theory of monoidal categories.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f8a5ed10d7f59fc2bd82de0dc61fac84
https://doi.org/10.1007/978-3-319-49834-8_1
https://doi.org/10.1007/978-3-319-49834-8_1
Autor:
Vladimir Turaev, Alexis Virelizier
Publikováno v:
Monoidal Categories and Topological Field Theory ISBN: 9783319498331
We define and study Hopf algebras in braided categories. This leads us to a useful re-formulation of the notion of a modular category and paves the way for the study of Hopf monads in the next chapters.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::27bdcbb770ce7e53c267814561180bf6
https://doi.org/10.1007/978-3-319-49834-8_6
https://doi.org/10.1007/978-3-319-49834-8_6
Autor:
Vladimir Turaev, Alexis Virelizier
Publikováno v:
Monoidal Categories and Topological Field Theory ISBN: 9783319498331
Ribbon graphs in a 3-manifold M generalize framed knots and links in M by allowing free ends lying in \(\partial \mathrm{M}\) and rectangular vertices lying in \(\mathrm{Int}(M)\;=\;M\partial M\). We define ribbon graphs in terms of so-called plexuse
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::07b0bc8081e9d71de86769937271396d
https://doi.org/10.1007/978-3-319-49834-8_14
https://doi.org/10.1007/978-3-319-49834-8_14
Autor:
Vladimir Turaev, Alexis Virelizier
Publikováno v:
Monoidal Categories and Topological Field Theory ISBN: 9783319498331
We derive from a spherical fusion category with invertible dimension a graph TQFT which applies to colored ribbon graphs in 3-dimensional cobordisms. For cobordisms with empty graphs, we recover the TQFT of Chapter 13.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::95348c3cbfbb58bbe1d0faa3c39907d0
https://doi.org/10.1007/978-3-319-49834-8_15
https://doi.org/10.1007/978-3-319-49834-8_15