Subgroups and Combinatorial Nonpositive Curvature

* 拟议的研究围绕着首席研究员对立体几何及其应用的浓厚兴趣而展开。*该提案的亮点包括以下内容：*1）Malnormal Special Quotient Theorem的真正新证明。2)一个显式的刻画类的群是虚拟的极限群。3)关于完全相对双曲并合的一个cutility结果。3）平方复形的一个新的和更一般的非正曲率形式。4)关于三维流形的一个具体而明确的虚曲率定理。5)一个证明树的乘积上紧格不可约性是泛有的建议。6)对特殊立方复形的虚代数运算的研究，它超出了在3-流形设置中获得的结果。7)对一致性理论的持续探索 * 9)探索增长差距。

***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.