R-局部空间的自等价群上的胞腔附着效应
The effect of cell-attachment on the group of self-equivalences of an R-localized space
摘要：
设R是具有最小不可逆素p的有理数的子环，X = X^{n} \cup_α（\bigcup_{j \in J} e^{q}）是J有限且q关于p小的胞腔附着，E（XR）表示R-局部化X_R的同伦自等价群.利用DG Lie模型构造了一个短正合序列0 \to \bigoplus_{j \in J} π_q（X^n）_R \to E（X_R）\to C^q \to 0其中C^q是GL_{|J|}（R）\times E（X^n_R）的子群.我们得到了类的幂零群E_*（X）的R-局部化的一个相关结果。我们推导出一些明确的计算，这两个群体的空间与几个细胞。
英文摘要：
Let R be a subring of the rationals with least non-invertible prime p. Let X = X^{n} \cup_α (\bigcup_{j \in J} e^{q}) be a cell attachment with J finite and q small with respect to p. Let E(X_R) denote the group of homotopy self-equivalences of the R-localization X_R. We use DG Lie models to construct a short exact sequence 0 \to \bigoplus_{j \in J}π_q(X^n)_R \to E(X_R) \to C^q \to 0 where C^q is a subgroup of GL_{|J|}(R) \times E(X^n_R). We obtain a related result for the R-localization of the nilpotent group E_*(X) of classes inducing the identity on homology. We deduce some explicit calculations of both groups for spaces with few cells.
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