homotopy typeoperatorK-theoryWe study the homotopy type of the space of the unitary group U-1(C-u*(|Z(n)|)) of the uniform Roe algebra C-u*(|Z(n)|) of Z(n). We show that the stabilizing map U-1(C-u*(|Z(n)|)) -> U-infinity(C-u*(|Z(n)|)) is a homotopy ...
Homotopy Group In subject area: Mathematics Homotopy groups Let M(X, Y) denote the set of continuous mappings between the topological spaces X and Y. Two mappings f, g ∈ M(X, Y) are called homotopic if there is a one-parameter family of mappings ft ∈ M(X, Y) depending continuously...
We describe explicit presentations of all stable and the first nonstable homotopy groups of the unitary groups. In particular, for each n >= 2 we supply n homotopic maps that each represent the (n-1)!-th power of a suitable generator of pi_2n(U(n)) = Z_{n!}. The product of ...
The n-th homotopy group of X, πn(X) is the set of homotopy classes of maps from the n-sphere Sn (the space of unit vectors in Rn+1) to X which send a fixed point in Sn (called the base point) to a fixed point in X. (If X is not path-connected, then we must specify ...
Gauge groupHomotopy typeSpecial unitary groupCP3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$...
Nontrivial elements of homotopy groups for unitary, orthogonal, and symplectic groups are givenexplicitly. In particular, (a) representatives of generators... AT Lundell,Y Tosa - 《Journal of Mathematical Physics》 被引量: 8发表: 1990年 Homotopy groups of symplectic groups and the quaternionic ...
Let M be a von Neumann algebra, f a faithful normal state and denote by M^f the fixed point algebra of the modular group of f. Let U_M and U_{M^f} be the unitary groups of M and M^f. In this paper we study the quotient U_M/U_{M^f} endowed with two natural topologies:...
We study the homotopy type of the space of the unitary group \\operatorname{U}_1(C^\\ast_u(|\\mathbb{Z}^n|)) \\operatorname{U}_1(C^\\ast_u(|\\mathbb{Z}^n|)) of the uniform Roe algebra C^\\ast_u(|\\mathbb{Z}^n|) C^\\ast_u(|\\mathbb{Z}^n|) of \\mathbb{Z...
Special unitary groupsK-theoryThe v 1-periodic homotopy groups can be roughly described as the portions of the actual homotopy groups localized at a prime p that are detected by K-theory. In 1991 Davis showed that if p is an odd prime, v 1 −1 π 2 k ( SU ( n ) ; p ) is ...
Also we shall deal mainly with the classical groups, and in particular, the orthogonal and unitary groups. Proposition 9 Suppose that G is a connected Lie group. (i) If G is compact and semi-simple, then π1(G) is finite. This implies that G˜ is still compact. (ii) π2(G) =...