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 ...
Cone-decompositions of the special unitary groups The sulfur trioxide-monopole--SO(3)-monopole--cobordism formula is an equality of the Donaldson invariant of a closed, smooth four-manifold, with a universal expression involving invariants of that manifold, its intersection form, and other homotopy ...
Although such a definition of the trace is very natural, the proof of the additivity of the trace is surprisingly long and unnatural. In the present paper results on the homotopy theory of unitary group U of M are used to obtain a new proof of the additivity. The periodicity theorem of ...
The ν1-Periodic Homotopy Groups of SU(n) at Odd Primes From the author’s introduction: Let p be an odd prime, and q=2(p-1). The p-primary v 1 -periodic homotopy groups of the special unitary group SU(n), denoted by v 1 -1 π * (SU(n)), are defined as a direct limit...
5.Time reversal T is not unitary.时间反演T不是幺正的。 6.Inverson of Circle: Into a circle, if the circle pass through inversion center O, it becomes a straight line.圆的反演:反演成一圆。但当圆通过反演中心时变成一直线。 7.Meanwhile, they perform "festive lantern opera".同时又有"花灯戏...
The homotopy type of the unitary group of Hilbert space ☆ Using topological uniform descent, we give necessary and sufficient conditions for Browder's theorem and Weyl's theorem to hold for an operator A. The two theorems are liable to fail for 2 × 2 operator matrices. In this paper, we...
In particular, he considers rational and integral cohomology rings, including torsion, unitary K-theory, Morava K-theory, Brown-Peterson cohomology, stable and unstable homotopy groups, mod p decomposition, the number of homotopy classes of multiplications, and Lyusternik-Shnirel'man category. More...
2 Homotopy types of PU(n)-gauge groups The projective unitary group PU(n) is defined as the quotient of U(n) by its centre Z(U(n))={λIn∣λ∈C and |λ|=1}≅U(1). In marked contrast with the orthogonal case, there is a homotopy equivalence between PU(n) and PSU(n) for...
“polynomial” in the sense that they assemble into a Taylor tower, the layers (differences between successive polynomial approximations) of which are determined by spectra with an action of an appropriate group; an orthogonal group for orthogonal calculus, and a unitary group for unitary calculus....
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...