Subgroups and Combinatorial Nonpositive Curvature

***拟议的研究围绕着首席研究员对立方体几何及其应用的浓厚兴趣展开。***该建议的亮点包括以下几点：******1)一个真正新的反常特商定理的证明。***2)关于群类的明确描述，这些群实际上是极限群。***3)一个完整的相对双曲汞合金的计算结果。3)一种新的更一般的方形复形的非正曲率形式。***4)三维流形的一个具体而显式的虚计算定理。***5)证明树的积中的紧格的不可约性是一般的。***6)特殊立方体配合物的虚拟代数纤维的研究——超越在3流形环境下的研究。***7)对相干统一理论的继续探索。***9)对增长差距的探索。

***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.