Related papers: The generalized Dehn twist along a figure eight
The purpose of this paper is to introduce the notion of loop groupoid associated to a groupoid. After studying the general properties of the loop groupoid, we show how this notion provides a very natural geometric interpretation for the…
A generalisation of discrete torsion is introduced in which different discrete torsion phases are considered for the different fixed points or twist fields of a twisted sector. The constraints that arise from modular invariance are analysed…
We show that in the mapping class group of a surface any relation between Dehn twists of the form T_x^j T_y^k = M (M a multitwist) is the lantern relation, and any relation of the form (T_x T_y)^k = M (where T_x commutes with M) is the…
This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem for them. The computation methods for their fundamental…
A corner in a map is an edge-vertex-edge triple consisting of two distinct edges incident to the same vertex. A corneration is a set of corners that covers every arc of the map exactly once. Cornerations in a dart-transitive map generalize…
Identifying parallel sides of a collection of Euclidean polygons yields a flat surface with cone points of angles multiples of 2 pi, naturally a compact Riemann surface but also an algebraic curve, and a hyperbolic surface. In general two…
We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged "convexly", which is…
Given a smooth curve defined over a field $k$ that admits a non-singular plane model over $\overline{k}$, a fixed separable closure of $k$, it does not necessarily have a non-singular plane model defined over the field $k$. We determine…
We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…
We discuss the geometry of the c-map from projective special K\"ahler to quaternionic K\"ahler manifolds using the twist construction to provide a global approach to Hitchin's description. As found by Alexandrov et al. and Alekseevsky et…
Let $N_{g,s}$ denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski obtained an explicit finite presentation for the mapping class group $M(N_{g,s})$ of the surface $N_{g,s}$, where…
We initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight…
In this paper, we use a result of Dahmani to show that the Euler class of some power subgroup (the subgroup normally generated by a fixed power of Dehn twist about a non-separating curve) is trivial inside the mapping class group of once…
The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to…
We consider the universal family $E_n^d$ of superelliptic curves: each curve $\Sigma_n^d$ in the family is a $d$-fold covering of the unit disk, totally ramified over a set $P$ of $n$ distinct points; $\Sigma_n^d\hookrightarrow E_n^d\to…
A non-trivial element of a group is a generalized torsion element if some products of its conjugates is the identity. The minimum number of such conjugates is called a generalized torsion order. We provide several restrictions for…
One way to better understand the smooth mapping class group of the 4-sphere would be to give a list of generators in the form of explicit diffeomorphisms supported in neighborhoods of submanifolds, in analogy with Dehn twists on surfaces.…
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…
A complete description of the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4 is given. As a by-product we get a positive relation among right hand Dehn twists in the mapping class group of a closed…
We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…