论文标题
Artin演示，三角形组和4个manifolds
Artin presentations, triangle groups, and 4-manifolds
论文作者
论文摘要
gonz {Á} lez-acu {ñ} a表明，Artin演示是封闭的，可定向的$ 3 $ manifold组的特征。 Winkelnkemper后来发现，每个Artin演示文稿都决定了平滑，紧凑，简单连接的$ 4 $ MANIFOLD。我们利用三角形组在两个发电机上找到所有介绍小组的ARTIN演示文稿。然后，我们确定所有光滑，封闭，简单地连接的$ 4 $ manifolds，其中最多有两个Betti编号，其中两个出现在Artin演示理论中。
Gonz{á}lez-Acu{ñ}a showed that Artin presentations characterize closed, orientable $3$-manifold groups. Winkelnkemper later discovered that each Artin presentation determines a smooth, compact, simply-connected $4$-manifold. We utilize triangle groups to find all Artin presentations on two generators that present the trivial group. We then determine all smooth, closed, simply-connected $4$-manifolds with second betti number at most two that appear in Artin presentation theory.
