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。 该提案的要点包括： 1)一个真正的新的证明异常特商定理。 2)虚极限群类的一个显式特征. 3)完全相对双曲型并合的一个新结果。3）平方复形非正曲率的一种新的更一般形式。 4)三维流形上一个具体而明确的虚流形定理。 5)关于树的乘积上紧格不可约性是泛有的一个证明。 6)对超出3-流形设置中获得的特殊立方体复合体的虚拟代数纤维化的研究。 7)对一致性统一理论的持续探索。 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.