相关论文: A calculus for branched spine of 3-manifolds

We deduce some formulas for the spin invariants of the connected sum of an arbitrary 4-manifold X, b^+ _2(X) > 0 $ with $\overline {CP^2}$ in terms of the spin invariants of $X$ and apply this to prove the Van de Ven conjecture.

The masses and residues of the triply heavy spin--3/2 baryons are calculated in framework of the QCD sum rule approach. The obtained results are compared with the existing theoretical predictions in the literature.

We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism,…

We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes…

The triple point numbers and the triple point spectrum of a closed 3-manifold were defined in (R. Vigara, Representaci\'on de 3-variedades por esferas de Dehn rellenantes, PhD Thesis, UNED 2006). They are topological invariants that give a…

We show that a hyperbolic $3$-manifold can be the cyclic branched cover of at most fifteen knots in $\mathbf{S}^3$. This is a consequence of a general result about finite groups of orientation preserving diffeomorphisms acting on…

We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to…

A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…

We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions.…

In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its…

We propose a new method for the numerical computation of the cut locus of a compact submanifold of $\mathbb{R}^3$ without boundary. This method is based on a convex variational problem with conic constraints, with proven convergence. We…

A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.

We calculate the RT-invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [V. G. Turaev, Quantum invariants of knots and 3--manifolds, de…

In this paper we first give a one-move version of Markov's braid theorem for knot isotopy in $S^3$ that sharpens the classical theorem. Then a relative version of Markov's theorem concerning a fixed braided portion in the knot. We also…

We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projections of isotopic links. We also show that any link admits a…

This essay explains an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as…

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…

We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.

We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we…

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct…