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Search: All articles in the CMB digital archive with keyword fundamental group

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1. CMB Online first

Clay, Adam; Desmarais, Colin; Naylor, Patrick
 Testing bi-orderability of knot groups We investigate the bi-orderability of two-bridge knot groups and the groups of knots with 12 or fewer crossings by applying recent theorems of Chiswell, Glass and Wilson. Amongst all knots with 12 or fewer crossings (of which there are 2977), previous theorems were only able to determine bi-orderability of 499 of the corresponding knot groups. With our methods we are able to deal with 191 more. Keywords:knots, fundamental groups, orderable groupsCategories:57M25, 57M27, 06F15

2. CMB 2015 (vol 58 pp. 787)

 Non-branching RCD$(0,N)$ Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups In this paper, we generalize the finite generation result of Sormani to non-branching $RCD(0,N)$ geodesic spaces (and in particular, Alexandrov spaces) with full support measures. This is a special case of the Milnor's Conjecture for complete non-compact $RCD(0,N)$ spaces. One of the key tools we use is the Abresch-Gromoll type excess estimates for non-smooth spaces obtained by Gigli-Mosconi. Keywords:Milnor conjecture, non negative Ricci curvature, curvature dimension condition, finitely generated, fundamental group, infinitesimally HilbertianCategories:53C23, 30L99

3. CMB 2013 (vol 57 pp. 439)

Yang, YanHong
 The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus-2 Curves $X$ in Charateristic $2$ We prove that for every ordinary genus-$2$ curve $X$ over a finite field $\kappa$ of characteristic $2$ with $\textrm{Aut}(X/\kappa)=\mathbb{Z}/2\mathbb{Z} \times S_3$, there exist $\textrm{SL}(2,\kappa[\![s]\!])$-representations of $\pi_1(X)$ such that the image of $\pi_1(\overline{X})$ is infinite. This result produces a family of examples similar to Laszlo's counterexample to de Jong's question regarding the finiteness of the geometric monodromy of representations of the fundamental group. Keywords:vector bundle, Frobenius pullback, representation, etale fundamental groupCategories:14H60, 14D05, 14G15

4. CMB 2003 (vol 46 pp. 122)

Moon, Myoungho
 On Certain Finitely Generated Subgroups of Groups Which Split Define a group $G$ to be in the class $\mathcal{S}$ if for any finitely generated subgroup $K$ of $G$ having the property that there is a positive integer $n$ such that $g^n \in K$ for all $g\in G$, $K$ has finite index in $G$. We show that a free product with amalgamation $A*_C B$ and an $\HNN$ group $A *_C$ belong to $\mathcal{S}$, if $C$ is in $\mathcal{S}$ and every subgroup of $C$ is finitely generated. Keywords:free product with amalgamation, $\HNN$ group, graph of groups, fundamental groupCategories:20E06, 20E08, 57M07
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