Editorial Manager(tm) for Journal of Knot Theory and Its Ramifications Manuscript Draft Manuscript Number: Title: CAT(0) STRUCTURES AND SUSPENDED ALTERNATING LINKS

We consider complements of links in the suspension of an orientable surface S of genus g > 0, and show that their fundamental groups naturally admit presentations which are analogues of Dehn presentations of classical link complements. For certain links, we show that they admit canonical cubings of non-positive curvature, and that certain groups admitting Dehn-like presentations contain closed surface subgroups. CAT(0) STRUCTURES AND SUSPENDED ALTERNATING LINKS Iain Aitchison and Lawrence Reeves Abstract. We consider complements of links in the suspension of an orientable surface S of genus g ≥ 0, and show that their fundamental groups naturally admit presentations which are analogues of Dehn presentations of classical link complements. For certain links, we show that they admit canonical cubings of non-positive curvature, and that certain groups admitting Dehn-like presentations contain closed surface subgroups. We consider complements of links in the suspension of an orientable surface S of genus g ≥ 0, and show that their fundamental groups naturally admit presentations which are analogues of Dehn presentations of classical link complements. For certain links, we show that they admit canonical cubings of non-positive curvature, and that certain groups admitting Dehn-like presentations contain closed surface subgroups.