Related Experiment Video
Updated: Aug 9, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds
1Department of Mathematics, Columbia University, New York, NY 10027.
Abstract:
Among other results, we rationally calculate the algebraic K-theory of any discrete cocompact subgroup of a Lie group G, where G is either O(n, 1), U(n, 1), Sp(n, 1), or F(4), in terms of the homology of the double coset space Gamma\G/K, where K is a maximal cocompact subgroup of G. We obtain the formula K(n)(ZGamma) [unk] [unk] congruent with [unk](i=0) (infinity)H(i)(Gamma\G/K; [unk](n-i)), where [unk](j) is a stratified system of Q vector spaces over Gamma\G/K and the vector space [unk](j)(GammagK) corresponding to the double coset GammagK is isomorphic to K(J)(Z(Gamma [unk] gKg(-1))) [unk] Q. Note Gamma [unk] gKg(-1) is a finite subgroup of Gamma. Earlier, a similar formula for discrete cocompact subgroups Gamma of the group of rigid motions of Euclidean space was conjectured by F. T. Farrell and W. C. Hsiang and proven by F. Quinn.
Related Concept Videos
Fundamental Theorem of Algebra
Hyperbolas
Geometry of Hyperbolas
Torsion in Vector Calculus
Space-Time Curvature and the General Theory of Relativity
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of motion,...
SFG Algebra
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
