Homotopy sequence of a topological groupoid with a basegroup and an obstruction to presentability of proper regular Lie groupoids

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• 作者：B. Jelenc ; J. Mr?un
• 关键词：Topological groupoids ; Morita category ; Homotopy groups ; Serre fibrations ; 22A22 ; 55Q05 ; 58H05
• 刊名：Journal of Homotopy and Related Structures
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：10
• 期：3
• 页码：519-536
• 全文大小：474 KB
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• 作者单位：B. Jelenc (1)
  J. Mr?un (2)
  
  1. Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000?, Ljubljana, Slovenia
  2. Department of Mathematics, University of Ljubljana, Jadranska 19, 1000?, Ljubljana, Slovenia
  
• 刊物主题：Algebraic Topology; Algebra; Functional Analysis; Number Theory;
• 出版者：Springer Berlin Heidelberg
• ISSN：1512-2891

文摘

A topological groupoid \(\fancyscript{G}\) is \(K\)-pointed, if it is equipped with a homomorphism from a topological group \(K\) to \(\fancyscript{G}\). We describe the homotopy groups of such \(K\)-pointed topological groupoids and relate these groups to the ordinary homotopy groups in terms of a long exact sequence. As an application, we give an obstruction to presentability of proper regular Lie groupoids. Keywords Topological groupoids Morita category Homotopy groups Serre fibrations