部分欧拉示性数、正规生成与稳定D（2）问题
Partial Euler Characteristic, Normal Generations and the stable D(2) problem
摘要：
研究了Wall的$D(2)$问题、完满群的正规生成猜想（Wiegold猜想）和Swan的关于群的部分欧拉示性数和亏数的问题之间的相互影响.特别地，对于上同调维数为2的3维复体$X$和有限基本群，假设Wiegold猜想成立，我们证明了X在楔入球面$S^2$的一个副本后同伦等价于一个有限2-复体.
英文摘要：
We study the interplay among Wall's $D(2)$ problem, normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and deficiency of groups. In particular, for a 3-dimensional complex $X$ of cohomological dimension 2 with a finite fundamental group, assuming the Wiegold conjecture holds, we prove that X is homotopy equivalent to a finite 2-complex after wedging a copy of sphere $S^2$.
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