Results 11 to 20 of about 154,233 (325)
On the growth of the homology of a free loop space [PDF]
Pure and Applied Mathematics Quarterly, 2013 We prove that for a wide class of spaces X the homology of the free loop space H∗(XS1;Q) has a very strong exponential growth. We call this convergence, controlled exponential growth, and we prove the good behavior of the controlled exponential growth with respect to fibrations.
Yves Félix +2 more
core +5 more sources
Aerospace, 2022 The proliferation of reusable space vehicles has fundamentally changed how assets are injected into the low earth orbit and beyond, increasing both the reliability and frequency of launches.
Marco Peterson +3 more
doaj +2 more sources
Development of 6DOF Hardware-in-the-Loop Ground Testbed for Autonomous Robotic Space Debris Removal
AerospaceThis paper presents the development of a hardware-in-the-loop ground testbed featuring active gravity compensation via software-in-the-loop integration, specially designed to support research in autonomous robotic removal of space debris.
Ahmad Al Ali +2 more
doaj +2 more sources
On the geometry of free loop spaces [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 We verify the following three basic results on the free loop space LM. (1) We show that the set of all points, where the fundamental form on LM is nondegenerate, is an open subset.
P. Manoharan
doaj +3 more sources
The free loop space of globally symmetric spaces
Inventiones Mathematicae, 1977 In the study of closed geodesics the free loop space A(M)={c: S1--,M} is a natural tool. It can be made into a Hilbert manifold and the energy integral is a C ~ function on A(M) whose critical points are the closed geodesics. Therefore Morse theory has been applied to find relationships between closed geodesics and the topology of A(M).
Wolfgang Ziller
exaly +3 more sources
Path space and free loop space
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011 The paper under review discusses the \(L^2\)-geometry of the space \(LM\) of smooth loops on a Riemannian manifold \(M\). It starts by recalling very basic facts and proceeds to a computation of the \(L^2\) covariant derivative and \(L^2\) curvature tensor of \(LM\), which is the main result claimed in the paper.
exaly +4 more sources
On the Borel cohomology of free loop spaces
MATHEMATICA SCANDINAVICA, 2003 Let $X$ be a space and let $K = H^*(X; \boldsymbol F_p)$ where $p$ is an odd prime. We construct functors $\overline \Omega$ and $\ell$ which approximate cohomology of the free loop space $\Lambda X$ as follows: There are homomorphisms $\overline \Omega(K) \to H^*(\Lambda X; \boldsymbol F_p)$ and $\ell(K)\to H^*(E\boldsymbol T\times_T\Lambda X ...
Iver Ottesen
openalex +5 more sources
On The Growth of the Homology of a Free Loop Space II [PDF]
Annales de l'Institut Fourier, 2017 Controlled exponential growth is a stronger version of exponential growth. We prove that the homology of the free loop space ℒ X has controlled exponential growth in two ...
Yves Félix +2 more
openalex +3 more sources
The cohomology ring of free loop spaces [PDF]
Homology, Homotopy and Applications, 2000 39 ...
Luc Menichi
openalex +5 more sources
A State-Space Framework for Parallelizing Digital Signal Processing in Coherent Optical Receivers [PDF]
SensorsUltra-high sampling rates in coherent optical front-ends increasingly exceed the processing capabilities of real-time baseband processors, creating a bottleneck in coherent free-space optical communication systems.
Jinyang Wang, Zhugang Wang, Di Liu
doaj +2 more sources