Quasisymmetric Nonparametrization and Spaces Associated with the Whitehead Continuum
نویسندگان
چکیده
The decomposition space R3/Wh associated with the Whitehead continuum Wh is not a manifold, but the product (R3/Wh) × Rm is homeomorphic to R3+m for any m ≥ 1 (known since the 1960’s). We study the quasisymmetric structure on (R3/Wh) × Rm and show that the space (R3/Wh) × Rm may be equipped with a metric resembling R3+m geometrically and measure theoretically—it is linearly locally contractible and Ahlfors (3 + m)-regular—nevertheless the resulting space does not admit a quasisymmetric parametrization by R3+m .
منابع مشابه
Geometry and Quasisymmetric Parametrization of Semmes Spaces
We consider decomposition spaces R/G that are manifold factors and admit defining sequences consisting of cubes-with-handles of finite type. Metrics on R/G constructed via modular embeddings of R/G into a Euclidean space promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R/G×R by R for any m ≥ 0 imposes quantitative topological con...
متن کاملQuasisymmetric Sewing in Rigged Teichmüller Space
One of the basic geometric objects in conformal field theory (CFT) is the moduli space of Riemann surfaces whose boundaries are “rigged” with analytic parametrizations. The fundamental operation is the sewing of such surfaces using the parametrizations. We generalize this picture to quasisymmetric boundary parametrizations. By using tools such as the extended λ-lemma and conformal welding we pr...
متن کاملA Comparison Between Fourier Transform Adomian Decomposition Method and Homotopy Perturbation ethod for Linear and Non-Linear Newell-Whitehead-Segel Equations
In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...
متن کاملUniversal Teichmüller Space
We present an outline of the theory of universal Teichmüller space, viewed as part of the theory of QS, the space of quasisymmetric homeomorphisms of a circle. Although elements of QS act in one dimension, most results about QS depend on a two-dimensional proof. QS has a manifold structure modelled on a Banach space, and after factorization by PSL(2,R) it becomes a complex manifold. In applicat...
متن کامل