幂零拟群

关于幂零与下中心同态映射的Quandle同态

On Nilpotent and Hypocentral Quandle Homomorphisms

本文为quandle满射同态定义幂零与下中心概念，证明其等价于覆盖同态复合及右正交性，建立正交分解系统，并给出约化同态的幂零充分条件。

Linking numbers, quandles and groups

We introduce a quandle invariant of classical and virtual links, denoted $Q_{tc} (L)$. This quandle has the property that $Q_{tc} (L) \cong Q_{tc} (L')$ if and only if the components of $L$ and $L'$ can be indexed in such a way that $L=K_1 \cup \dots \cup K_μ$, $L'=K'_1 \cup \dots \cup K'_μ$ and for each index $i$, there is a multiplier $ε_i \in \{-1,1\}$ that connects virtual linking numbers over $K_i$ in $L$ to virtual linking numbers over $K'_i$ in $L'$: $\ell_{j/i}(K_i,K_j)= ε_i \ell_{j/i}(K'_i,K'_j)$ for all $j \neq i$. We also extend to virtual links a classical theorem of Chen, which re…

Filling inequalities for nilpotent groups

We bound the higher-order Dehn functions and other filling invariants of certain Carnot groups using approximation techniques. These groups include the higher-dimensional Heisenberg groups, jet groups, and central products of two-step nilpotent groups. Some consequences of this work are a construction of groups with arbitrarily large nilpotency class that have euclidean n-dimensional filling volume functions, and a proof of part of a conjecture of Gromov on the higher-order filling functions of the higher-dimensional Heisenberg groups.

Fixed points of discrete nilpotent group actions on S^2

We prove that for each integer k of at least 2, there is an open neigborhood ν_k of the identity map of the 2-sphere S^2, in C^1-topology such that: if G is a nilpotent subgroup of Diff^1(S^2) with length k of nilpotency, generated by elements in ν_k, then the natural action on S^2 has non-empty fixed point set. Moreover, the G-action has at least two fixed points if the action has a finite non-trivial orbit.

关于幂零群中心积的Dehn函数

On the Dehn functions of central products of nilpotent groups

本文确定了多类幂零李群中心积的Dehn函数，证实了相关猜想，并构造了无限族群使Cornulier的界渐近最优。