CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

On $3$-manifolds with Torus or Klein Bottle Category Two

  Published:2013-10-12
 Printed: Sep 2014
  • Wolfgang Heil,
    Department of Mathematics, Florida State University, Tallahassee, Florida 32306
  • Dongxu Wang,
    Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   LaTeX   MathJax   PDF  

Abstract

A subset $W$ of a closed manifold $M$ is $K$-contractible, where $K$ is a torus or Kleinbottle, if the inclusion $W\rightarrow M$ factors homotopically through a map to $K$. The image of $\pi_1 (W)$ (for any base point) is a subgroup of $\pi_1 (M)$ that is isomorphic to a subgroup of a quotient group of $\pi_1 (K)$. Subsets of $M$ with this latter property are called $\mathcal{G}_K$-contractible. We obtain a list of the closed $3$-manifolds that can be covered by two open $\mathcal{G}_K$-contractible subsets. This is applied to obtain a list of the possible closed prime $3$-manifolds that can be covered by two open $K$-contractible subsets.
Keywords: Lusternik--Schnirelmann category, coverings of $3$-manifolds by open $K$-contractible sets Lusternik--Schnirelmann category, coverings of $3$-manifolds by open $K$-contractible sets
MSC Classifications: 57N10, 55M30, 57M27, 57N16 show english descriptions Topology of general $3$-manifolds [See also 57Mxx]
Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
Invariants of knots and 3-manifolds
Geometric structures on manifolds [See also 57M50]
57N10 - Topology of general $3$-manifolds [See also 57Mxx]
55M30 - Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
57M27 - Invariants of knots and 3-manifolds
57N16 - Geometric structures on manifolds [See also 57M50]
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/