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In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
It is known that viewing the fundamental group 1(X) as the quotient space of X does not always give rise to a topological group.
Geometry of Topological Defects of Two-dimensional Sigma Models
Geometry of Topological Defects Two-dimensional Sigma Models
2010/12/16
A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of ...
Topological invariants from non-restricted quantum groups
Topological invariants non-restricted quantum groups
2010/12/9
We introduce the notion of a relative spherical category. We prove that such a category
gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants de ned in [12] and [17], respe...
On fuzzy topological ring valued fuzzy continuous functions
fuzzy topological ring (FTR) fuzzy ideal
2010/9/13
The collection of all fuzzy continuous functions from a fts Y to a fuzzy topological ring (in short, FTR) Z, denoted by FC(Y,Z) induces a ring structure from that of Z. This paper explores the structu...
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
Topological expansion of beta-ensemble model quantum algebraic geometry sectorwise approach
2010/12/14
We solve the loop equations of the β-ensemble model analogously to the solution found for the Hermitian matrices β = 1. For β = 1, the solution was expressed using the algebraic spectral curve of equa...
A Topological Degree Counting for some Liouville Systems of Mean Field Equations
Topological Degree some Liouville Systems of Mean Field Equations
2010/11/26
Let A = (aij)n×n be an invertible matrix and A−1 =(aij )n×n be the inverse of A. In this paper.
A Topological Version of the Borel-Tits Theorem on Abstract Homomorphisms of Simple Algebraic Groups
Topological Version Borel-Tits Theorem Simple Algebraic Groups
2010/12/9
In this paper, we produce topologized versions of two theorems. One is due to Borel and Tits [2] and is concerned with abstract homomorphisms of absolutely almost simple algebraic groups.
On H-groups and their applications to topological homotopy groups
H-group sub-H-group loop space Topological homotopy
2010/12/13
This paper develops a basic theory of H-groups. We intro-duce a special quotient of H-groups and extend some algebraic construc-tions of topological groups to the category of H-groups and H-maps. We u...
Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves
Topological recursion Poincare polynomial combinatorial moduli space of curves
2010/12/3
We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satis es a topological
recursion formu...
The Kontsevich constants for the volume of the moduli of curves and topological recursion
Kontsevich constants volume of the moduli of curves topological recursion
2010/12/3
We give an Eynard-Orantin type topological recursion formula for the canonical Euclidean
volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion
comes from the edg...
The ground state degeneracy of an SU(N)k topological phase with n quasiparticle excitations is
relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an
open que...
We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which...
Higher topological complexity and homotopy dimension of configuration spaces on spheres
Lusternik-Schnirelmann category Schwarz genus topological complexity configuration spaces hyperplane arrangements
2010/12/3
In the paper “On Higher Analogs of Topological Complexity”Yu. Rudyak introduced the concept of TCn(X), the nth topological complexity of a path-connected space X. This concept was developed as a gener...
Topological optimisation of rod-stirring devices
Topological optimisation rod-stirring devices
2010/4/6
There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly stretch a material such as bread dough or taffy. The goal in these applications is to stretch either ...