Browsing 1 - Oberwolfach Preprints (OWP) by MSC "57"
Now showing items 1-17 of 17
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Braid equivalences and the L-moves
[OWP-2011-20] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-19)In this survey paper we present the L-moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots ... -
Braidoids
[OWP-2020-17] (Mathematisches Forschungsinstitut Oberwolfach, 2020-09-03)Braidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce the notion of braidoids in ... -
The Colored Jones Polynomial and Kontsevich-Zagier Series for Double Twist Knots
[OWP-2017-29] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-20)Using a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots $K_{(-m,-p)}$ and $K_{(-m,p)}$ where $m$ and $p$ are positive integers. In the $(-m,-p)$ case, this leads to new ... -
A construction of hyperbolic Coxeter groups
[OWP-2010-04] (Mathematisches Forschungsinstitut Oberwolfach, 2010)We give a simple construction of Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension. Our construction provides new examples of such groups. Using this one can construct e.g. new groups ... -
Embedding Spaces of Split Links
[OWP-2022-13] (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-01)We study the homotopy type of the space $\mathcal{E}(L)$ of unparametrised embeddings of a split link $L=L_1\sqcup \ldots \sqcup L_n$ in $\mathbb{R}^3$. Inspired by work of Brendle and Hatcher, we introduce a semi-simplicial ... -
Graphical constructions for the sl(3), C2 and G2 invariants for virtual knots, virtual braids and free knots
[OWP-2015-13] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-31)We construct graph-valued analogues of the Kuperberg sl(3) and $G_2$ invariants for virtual knots. The restriction of the sl(3) and $G_2$ invariants for classical knots coincides with the usual Homflypt sl(3) invariant and ... -
Invariant Four-forms and Symmetric Pairs
[OWP-2012-03] (Mathematisches Forschungsinstitut Oberwolfach, 2012-04-24)We give criteria for real, complex and quaternionic representations to define $s$-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of ... -
Legendrian Knots in Lens Spaces
[OWP-2011-01] (Mathematisches Forschungsinstitut Oberwolfach, 2011)In this note, we first classify all topological torus knots lying on the Heegaard torus in Lens spaces, and then we classify Legendrian representatives of torus knots. We show that all Legendrian torus knots in universally ... -
Legendrian Lens Space Surgeries
[OWP-2016-10] (Mathematisches Forschungsinstitut Oberwolfach, 2016-06-17)We show that every tight contact structure on any of the lens spaces $L(ns^2 - s + 1,s^2)$ with $n\geq 2, s \geq 1$, can be obtained by a single Legendrian surgery along a suitable Legendrian realisation of the negative ... -
Legendrian rational unknots in lens spaces
[OWP-2013-06] (Mathematisches Forschungsinstitut Oberwolfach, 2013-03-14)We classify Legendrian rational unknots with tight complements in the lens spaces $L(p,1)$ up to coarse equivalence. As an example of the general case, this classification is also worked out for $L(5, 2)$. The knots are ... -
Mesh Ratios for Best-Packing and Limits of Minimal Energy Configurations
[OWP-2013-13] (Mathematisches Forschungsinstitut Oberwolfach, 2013-06-10)For $N$-point best-packing configurations $\omega_N$ on a compact metric space $(A, \rho)$, we obtain estimates for the mesh-separation ratio $\gamma(\rho_N , A)$, which is the quotient of the covering radius of $\omega_N$ ... -
On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces
[OWP-2013-18] (Mathematisches Forschungsinstitut Oberwolfach, 2013-07-23)Let $\Sigma_g$ be a closed hyperbolic surface of genus $g$ and let Ham($\Sigma_ g$) be the group of Hamiltonian diffeomorphisms of $\Sigma_g$. The most natural word metric on this group is the autonomous metric. It has ... -
On the geometry of regular maps from a quasi-projective surface to a curve
[OWP-2013-03] (Mathematisches Forschungsinstitut Oberwolfach, 2013-03-14)We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X. -
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
[OWP-2011-32] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic ... -
Singularities and Bifurcations of Pseudospherical Surfaces
[OWP-2020-08] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-17)We study singularities and bifurcations of constant negative curvature surfaces in Euclidean 3-space via their association with Lorentzian harmonic maps. This preprint presents the basic results on this, the full proofs ... -
Weakly Complex Homogeneous Spaces
[OWP-2012-04] (Mathematisches Forschungsinstitut Oberwolfach, 2012-04-24)We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous ... -
Z2-Thurston Norm and Complexity of 3-Manifolds, II
[OWP-2017-36] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-20)In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3-manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we ...