Subgroups and Combinatorial Nonpositive Curvature

该研究计划围绕首席研究员对立体几何及其应用的浓厚兴趣展开。该计划的重点包括以下内容：1）Malnormal Special Quotient Theorem的一个真正的新证明; 2）一类群是虚拟极限群的一个明确的特征; 3）完全相对双曲并合的一个cumbery结果; 3）平方复形的一个新的和更一般的非正曲率形式; 4）3-流形的一个具体的和明确的虚拟cumbery定理; 5）证明树的乘积中的余紧格的不可约性是泛有的一个建议。6）对三维流形上特殊立方体复形的虚代数表示的研究。7）对相干统一理论的继续探索。9）对生长间隙的探索。

The proposed research circulates around the principal investigator's deep interest in cubical geometry and its applications.Highlights of the proposal include the following:1) A genuinely new proof of the Malnormal Special Quotient Theorem.2) An explicit characterization of the class of groups that are virtually limit groups.3) A cubulation result for full relatively hyperbolic amalgams.3) A new and more general form of nonpositively curvature for square complexes.4) A concrete and explicit virtual cubulation theorem for 3-manifolds.5) A proposal to prove that irreducibilty is generic for cocompact lattices in the products of trees.6) An investigation of virtual algebraic fibering for special cube complexes beyond that obtained in the 3-manifold setting.7) A continued search for a unified theory of coherence.9) An exploration of growth-gaps.