CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 57N10 ( Topology of general $3$-manifolds [See also 57Mxx] )

  Expand all        Collapse all Results 1 - 3 of 3

1. CMB 2013 (vol 57 pp. 526)

Heil, Wolfgang; Wang, Dongxu
On $3$-manifolds with Torus or Klein Bottle Category Two
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
Categories:57N10, 55M30, 57M27, 57N16

2. CMB 1999 (vol 42 pp. 257)

Austin, David; Rolfsen, Dale
Homotopy of Knots and the Alexander Polynomial
Any knot in a 3-dimensional homology sphere is homotopic to a knot with trivial Alexander polynomial.

Categories:57N10, 57M05, 57M25, 57N65

3. CMB 1997 (vol 40 pp. 370)

Rolfsen, Dale; Zhongmou, Li
Which $3$-manifolds embed in $\Triod \times I \times I$?
We classify the compact $3$-manifolds whose boundary is a union of $2$-spheres, and which embed in $T \times I \times I$, where $T$ is a triod and $I$ the unit interval. This class is described explicitly as the set of punctured handlebodies. We also show that any $3$-manifold in $T \times I \times I$ embeds in a punctured handlebody.

Categories:57N10, 57N35, 57Q35

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