1-loop graphs and configuration space integral for embedding spaces
نویسندگان
چکیده
منابع مشابه
Configuration Space Integrals for Embedding Spaces and the Haefliger Invariant
Let Kn,j be the space of long j-knots in R . In this paper we introduce a graph complex D∗ and a linear map I : D∗ → Ω∗DR(Kn,j) via configuration space integral, and prove that (1) when both n > j ≥ 3 are odd, I is a cochain map if restricted to graphs with at most one loop component, (2) when n− j ≥ 2 is even, I is a cochain map if restricted to tree graphs, and (3) when n− j ≥ 3 is odd, I add...
متن کاملOn Loop Spaces of Configuration Spaces
This article gives an analysis of topological and homological properties for loop spaces of configuration spaces. The main topological results are given by certain choices of product decompositions of these spaces, as well as “twistings” between the factors. The main homological results are given in terms of extensions of the “infinitesimal braid relations” or “universal YangBaxter Lie relations”.
متن کاملConfiguration spaces on the sphere and higher loop spaces
We show that the homology over a field of the space ΛnΣnX of free maps from the n-sphere to the n-fold suspension of X depends only on the cohomology algebra of X and compute it explicitly. We compute also the homology of the closely related labelled configuration space C(Sn, X) on the n-sphere with labels in X and of its completion, that depends only on the homology of X. In many but not all c...
متن کاملEmbedding rotations in translational configuration space
This paper presents the graphical embeding of the rotational degree of freedom into the translational Configuration Space for planar assembly tasks. The resulting representation helps the visualization and understanding of motions in a simple and easy graphical way. The aim is the developing of motion planning algorithms in a two-dimensional parametrized space for planar assembly tasks (3 d.o.f...
متن کاملThe Configuration Space Integral for Links and Tangles in R
The perturbative expression of Chern-Simons theory for links in Euclidean 3-space is a linear combination of integrals on configuration spaces. This has successively been studied by Guadagnini, Martellini and Mintchev, Bar-Natan, Kontsevich, Bott and Taubes, D. Thurston, Altschuler and Freidel, Yang. . .We give a self-contained version of this study with a new choice of compactification, and we...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2012
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004111000429