scholarly journals Homotopical and operator algebraic twisted K-theory

2020 ◽  
Vol 378 (3-4) ◽  
pp. 1021-1059
Author(s):  
Fabian Hebestreit ◽  
Steffen Sagave
Keyword(s):  
Homotopy Theory ◽  
Complex Case ◽  
Joint Work ◽  
The Real ◽  
Comparison Results ◽  
Algebraic Constructions ◽  
K Theory ◽  
Multiplicative Structures

Abstract Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real and complex case. We also improve several comparison results about twisted K-theory of $$C^*$$ C ∗ -algebras to include multiplicative structures. Our results can also be interpreted in the $$\infty $$ ∞ -categorical setup for parametrized spectra.

Projection constants of symmetric spaces and variants of Khintchine's inequality

1999 ◽  
Vol 1999 (511) ◽  
pp. 1-42 ◽  
Author(s):  
Hermann König ◽  
Carsten Schütt ◽  
Nicole Tomczak-Jaegermann
Keyword(s):  
Symmetric Spaces ◽  
Dimensional Space ◽  
Complex Case ◽  
Real Case ◽  
The Real ◽  
Symmetric Basis ◽  
Projection Constant ◽  
Khintchine’S Inequality ◽  
Averaging Techniques

Abstract The projection constants of the lpn-spaces for 1 ≦ p ≦ 2 satisfy with in the real case and in the complex case. Further, there is c < 1 such that the projection constant of any n-dimensional space Xn with 1-symmetric basis can be estimated by . The proofs of the results are based on averaging techniques over permutations and a variant of Khintchine's inequality which states that

scholarly journals On the K-theory of the loop space of a Lie group

1974 ◽  
Vol 76 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Francis Clarke
Keyword(s):  
Lie Group ◽  
Loop Space ◽  
Simple Structure ◽  
Homology Theory ◽  
Compact Lie Group ◽  
Classifying Space ◽  
K Theory ◽  
Simply Connected ◽  
Torsion Free ◽  
Multiplicative Structures

Let G be a simply connected, semi-simple, compact Lie group, let K* denote Z/2-graded, representable K-theory, and K* the corresponding homology theory. The K-theory of G and of its classifying space BG are well known, (8),(1). In contrast with ordinary cohomology, K*(G) and K*(BG) are torsion-free and have simple multiplicative structures. If ΩG denotes the space of loops on G, it seems natural to conjecture that K*(ΩG) should have, in some sense, a more simple structure than H*(ΩG).

scholarly journals Generalized Givens Rotations Applied to Complex Joint Eigenvalue Decomposition

2021 ◽  
Vol 1 (1) ◽  
pp. 58-62
Author(s):  
Ammar Mesloub
Keyword(s):  
Complex Case ◽  
Eigenvalue Decomposition ◽  
Real Case ◽  
Joint Diagonalization ◽  
The Real ◽  
Givens Rotation ◽  
Givens Rotations ◽  
Simulation Results ◽  
Complex Joint

This paper shows the different ways of using generalized Givens rotations in complex joint eigenvaluedecomposition (JEVD) problem. It presents the different schemes of generalized Givens rotation, justifies the introducedapproximations and focuses on the process of extending an algorithm developed for real JEVD to the complex JEVD.Several Joint Diagonalization problem use generalized Givens rotations to achieve the solution, many algorithmsdeveloped in the real case exist in the literature and are not generalized to the complex case. Hence, we show herein asimple and not trivial way to get the complex case from the real one. Simulation results are provided to highlight theeffectiveness and behaviour of the proposed techniques for different scenarios.

scholarly journals Monodromy and K-theory of Schubert curves via generalized jeu de taquin

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Maria Monks Gillespie ◽  
Jake Levinson
Keyword(s):  
Local Algorithm ◽  
Jeu De Taquin ◽  
Bijective Correspondence ◽  
One Dimensional ◽  
The Real ◽  
Real Locus ◽  
Real Geometry ◽  
International Audience ◽  
K Theory ◽  
Rational Normal Curve

International audience We establish a combinatorial connection between the real geometry and the K-theory of complex Schubert curves Spλ‚q, which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal curve. In a previous paper, the second author showed that the real geometry of these curves is described by the orbits of a map ω on skew tableaux, defined as the commutator of jeu de taquin rectification and promotion. In particular, the real locus of the Schubert curve is naturally a covering space of RP1, with ω as the monodromy operator.We provide a fast, local algorithm for computing ω without rectifying the skew tableau, and show that certain steps in our algorithm are in bijective correspondence with Pechenik and Yong's genomic tableaux, which enumerate the K-theoretic Littlewood-Richardson coefficient associated to the Schubert curve. Using this bijection, we give purely combinatorial proofs of several numerical results involving the K-theory and real geometry of Spλ‚q.

scholarly journals Algebraic K-theory and abstract homotopy theory

2011 ◽  
Vol 226 (4) ◽  
pp. 3760-3812 ◽  
Author(s):  
Andrew J. Blumberg ◽  
Michael A. Mandell
Keyword(s):  
Homotopy Theory ◽  
K Theory ◽  
Abstract Homotopy Theory

Stable operations in mod p K-theory

1967 ◽  
Vol 63 (3) ◽  
pp. 631-646 ◽  
Author(s):  
C. R. F. Maunder
Keyword(s):  
Homotopy Theory ◽  
Cohomology Theory ◽  
Stable Homotopy ◽  
Stable Homotopy Theory ◽  
The Subject ◽  
Cohomology Operations ◽  
K Theory ◽  
Mod P

There comes a time in the development of a cohomology theory when a discussion of cohomology operations becomes necessary. In the case of complex K-theory, the subject of the present paper, such operations have of course already been investigated by Adams (see (2)), so that any further discussion might appear superfluous. Powerful as Adams's results are, however, the situation still leaves something to be desired: it is not known just what other operations can be defined in K-theory, and it is an inconvenience from the standpoint of stable homotopy theory that Adams's operations are not themselves stable.

scholarly journals Real Time Safety Model for Pedestrian Red-Light Running at Signalized Intersections in China

2021 ◽  
Vol 13 (4) ◽  
pp. 1695
Author(s):  
Yao Wu ◽  
Yanyong Guo ◽  
Wei Yin
Keyword(s):  
Real Time ◽  
Traffic Control ◽  
Red Light ◽  
Volume Ratio ◽  
Pedestrian Safety ◽  
Traffic Data ◽  
Red Light Running ◽  
The Real ◽  
Comparison Results ◽  
Safety Models

The traditional way to evaluate pedestrian safety is a reactive approach using the data at an aggregate level. The objective of this study is to develop real-time safety models for pedestrian red-light running using the signal cycle level traffic data. Traffic data for 464 signal cycles during 16 h were collected at eight crosswalks on two intersections in the city of Nanjing, China. Various real-time safety models of pedestrian red-light running were developed based on the different combination of explanatory variables using the Bayesian Poisson-lognormal (PLN) model. The Bayesian estimation approach based on Markov chain Monte Carlo simulation is utilized for the real-time safety models estimates. The models’ comparison results show that the model incorporated exposure, pedestrians’ characteristics and crossing maneuver, and traffic control and crosswalk design outperforms the model incorporated exposure and the model incorporated exposure, pedestrians’ characteristics, and crossing maneuver. The result indicates that including more variables in the real-time safety model could improve the model fit. The model estimation results show that pedestrian volume, ratio of males, ratio of pedestrians on phone talking, pedestrian waiting time, green ratio, signal type, and length of crosswalk are statistically significantly associated with the pedestrians’ red-light running. The findings from this study could be useful in real-time pedestrian safety evaluation as well as in crosswalk design and pedestrian signal optimization.

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