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pro vyhledávání: '"Bobtcheva, Ivelina"'
In this paper, we give a new direct proof of a result by Bobtcheva and Piergallini that provides finite algebraic presentations of two categories, denoted $3\mathrm{Cob}$ and $4\mathrm{HB}$, whose morphisms are manifolds of dimension $3$ and $4$, res
Externí odkaz:
http://arxiv.org/abs/2312.15986
Autor:
Bobtcheva, Ivelina
We prove that $S^1$ is a unimodular, cocommutative Hopf algebra in the category $CW^{1+1}$ of 2-equivalence classes of cobordisms of 2-dimensional CW-complexes and that $CW^{1+1}$ is actually equivalent to the symmetric monoidal category freely gener
Externí odkaz:
http://arxiv.org/abs/2309.04830
Autor:
Bobtcheva, Ivelina
It is proved in \cite{BP} (arXiv:1108.2717) that the category of relative 3-dimensional cobordisms $\cal Cob^{2+1}$ is equivalent to the universal algebraic category $\overline{\overline{\cal H}}{}^r$ generated by a Hopf algebra object. A different a
Externí odkaz:
http://arxiv.org/abs/2008.06706
We show that for any n > 3 there exists an equivalence functor from the category of n-fold connected simple coverings of B^3 x [0, 1] branched over ribbon surface tangles up to certain local ribbon moves, to the category Chb^{3+1} of orientable relat
Externí odkaz:
http://arxiv.org/abs/1108.2717
This paper is the second part of our work on 4-dimensional 2-handlebodies. In the first part (arXiv:math.GT/0407032) it is shown that up to certain set of local moves, connected simple coverings of B^4 branched over ribbon surfaces, bijectively repre
Externí odkaz:
http://arxiv.org/abs/math/0612806
We show that simple coverings of B^4 branched over ribbon surfaces up to certain local ribbon moves bijectively represent orientable 4-dimensional 2-handlebodies up to handle sliding and addition/deletion of cancelling handles. As a consequence, we o
Externí odkaz:
http://arxiv.org/abs/math/0407032
Publikováno v:
Algebr. Geom. Topol. 3 (2003) 33-87
The HKR (Hennings-Kauffman-Radford) framework is used to construct invariants of 4-thickenings of 2-dimensional CW complexes under 2-deformations (1- and 2- handle slides and creations and cancellations of 1-2 handle pairs). The input of the invarian
Externí odkaz:
http://arxiv.org/abs/math/0206307
Autor:
Bobtcheva, Ivelina, Quinn, Frank
We show that the Reshetikhin-Turaev-Walker invariant of 3-manifolds can be normalized to obtain an invariant of 4-dimensional thickenings of 2-complexes. Moreover when the underlying semisimple tortile category comes from the representations of a qua
Externí odkaz:
http://arxiv.org/abs/math/0012212
Autor:
Bobtcheva, Ivelina
Publikováno v:
Contemporary Math. 233 (1999), 69-95
Given a semisimple stable autonomous tensor category over a field $K$, to any group presentation with finite number of generators we associate an element $Q(P)\in K$ invariant under the Andrews-Curtis moves. We show that in fact, this is the same inv
Externí odkaz:
http://arxiv.org/abs/math/0012121
Autor:
Bobtcheva, Ivelina
In this work we set up a general framework for exact computations of the associativity, commutativity and duality morphisms in a quite general class of tortile categories. The source of the categories we study is the work of Gelfand and Kazhdan, Exam
Externí odkaz:
http://hdl.handle.net/10919/37995
http://scholar.lib.vt.edu/theses/available/etd-06062008-151240/
http://scholar.lib.vt.edu/theses/available/etd-06062008-151240/