Generalized universal covering spaces and the shape group
نویسندگان
چکیده
منابع مشابه
The Fundamental Group and Covering Spaces
These notes, from a first course in algebraic topology, introduce the fundamental group and the fundamental groupoid of a topological space and use them to classify covering spaces.
متن کاملSymplectic Group Actions and Covering Spaces
For symplectic group actions which are not Hamiltonian there are two ways to define reduction. Firstly using the cylinder-valued momentum map and secondly lifting the action to any Hamiltonian cover (such as the universal cover), and then performing symplectic reduction in the usual way. We show that provided the action is free and proper, and the Hamiltonian holonomy associated to the action i...
متن کاملOn the Universal Covering Space and the Fundamental Group
In this note it will be shown that when A is a retract (cf. [3])1 of X, then the same relationship holds between the universal covering spaces of A and X (Theorem 1.1) and also between the fundamental groups of A and X (Theorem 2.2). We denote the universal covering space of X by X*, where pEX, and the fundamental group by iriX) [l]. All spaces are assumed to be arcwise connected, Hausdorff spa...
متن کاملThe Universal Covering Group of U(n) and Projective Representations
Using fibre bundle theory we construct the universal covering group of U(n), Ũ(n), and show that Ũ(n) is isomorphic to the semidirect product SU(n)©s R. We give a bijection between the set of projective representations of U(n) and the set of equivalence classes of certain unitary representations of SU(n) ©s R. Applying Bargmann’s theorem, we give explicit expressions for the liftings of project...
متن کاملSome Algebraic Properties of Universal and Regular Covering Spaces
Let X̃ be a connected space, X be a space, let p : X̃ −→ X be a continuous map and let (X̃, p) be a covering space of X . In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X̃, p) of X and also their automorphism groups A(X̃, p). Keywords—covering ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2007
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm197-0-7