Related papers: Orbifoldization, covering surfaces and uniformizat…
The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold and orbifold embedding and provide many examples.…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
This article is devoted to the geometric construction which states a natural correspondence between topological coverings of a foliated manifolds and noncommutative coverings of the operator algebras. However this correspondence is not one…
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
We obtain an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points, and conjecture this to be true for an arbitrary number of ramification…
Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.
For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…
Orbifolds of two-dimensional quantum field theories have a natural formulation in terms of defects or domain walls. This perspective allows for a rich generalisation of the orbifolding procedure, which we study in detail for the case of…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
Torus orbifolds are topological generalization of symplectic toric orbifolds. We give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using toric topological method. As a result,…
Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold…
The concept of orbifolds should unify differential geometry with equivariant homotopy theory, so that orbifold cohomology should unify differential cohomology with proper equivariant cohomology theory. Despite the prominent role that…
This is a research announcement of the theory of orbifold quantum cohomology.
We formulate conjectures regarding percolation on planar triangulations suggested by assuming (quasi) invariance under coarse conformal uniformization.
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…
We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
We develop the theory of $H$-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of $H$-graded coverings of supermanifolds in the case where…
This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…