Description

• Title:
  Configuration spaces on punctured manifolds
• Creator:
  Fadell, Edward;
  Husseini, Sufian
• Description:
  The object here is to study the following question in the homotopy theory of configuration spaces of a general manifold $M$: When is the fibration $\mathbb F_{k+1}(M)\rightarrow\mathbb F_r(M)$, $r< k+1$, fiber homotopically trivial? The answer to this question for the special cases when $M$ is a sphere or euclidean space is given in [E. Fadell and S. Husseini, < i> Geometry and Topology of Configuration Spaces< /i> , Springer, New York, 2001]. The key to the solution of the problem for compact manifolds $M$ is the study of an associated question for the punctured manifold $M-q$, where $q$ is a point of $M$. The fact that $M-q$ admits a nonzero vector field plays a crucial role. Also required are investigations into the Lie algebra $\pi_*(\mathbb F_{k+1}(M))$, with special attention to the punctured case $\pi_*(\mathbb F_k(M-q))$. This includes the so-called Yang-Baxter equations in homotopy, taking into account the homotopy group elements of $M$ itself as well as the classical braid elements.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2002.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 20, No 1 (September 2002); 25 - 42;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.023/9635
• Subject:
  Configuration spaces;
  manifolds;
  fiberwise homotopy trivial;
  20F36;
  55R10;
  58B05;
  58E05;
  70G10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.023
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other