Subgroups and Combinatorial Nonpositive Curvature

这项拟议的研究围绕着首席研究员对三次几何及其应用的浓厚兴趣展开。 该建议的要点包括： 1)反常特商定理的一个新证明。 2)给出了一类实际上是极限群的群的显式刻画。 3)完全相对双曲拼图的一个立方结果。3)正方形复数非正曲率的一种新的更一般的形式。 4)3-流形的一个具体的显式虚拟孵化定理。 5)证明树的乘积中的余紧格的不可约性是一般的。 6)研究了除三维流形外的特殊立方体复形的虚拟代数纤维。 7)继续寻求统一的连贯理论。 9)对成长差距的探索。

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.