论文标题
关于完美链代数的准同态类型
On the quasi-isomorphism type of a perfect chain algebra
论文作者
论文摘要
令$ r $为A（p.i.d），让$ t（v），\ partial）$为免费$ r $ -dga。 $（t（v），\ partial）$的准同态类型是所有免费dgas的$ \ {（t（v），\ partial）\} $的$ \ {（t（v），\ partial）\} $，是quasi-iSomorphic to $（t（v），\ partial）$的所有免费dgas。在本文中，我们调查以表征和计算集合$ \ {（t（v），\ partial）\} $，用于新的免费DGA，称为Perfect（一种特殊的Perfect DGA是Adams-Hilton的Adams-Hilton模型），简单地连接了CW-Complex，以便$ h _ {*}（x，x，R）$是免费的。我们表明，如果$（t（v），\ partial）$和$（t（w），δ）$是两个完美的dgas，则$（t（w），δ）\ in \ {（t（v），\ partial）\} $，仅当它们的白头精确序列是同位序列。此外，我们表明，每个dga $（t（v），\ partial）$都可以分开以给出一对$ \ big（（（t（v），\ widetilde {\ partial}）），（π_{n}）_ {n \ geq 2} \ geq 2} \ big）与完美的dga $（t（v）$（t（t）扩展$（π_{n}）_ {n \ geq 2} $，我们确定如果$（t（w），\widetildeδ）\ in \ in \ {（t（v），\ wideTilde {\ partial}） $（π'_{n}）_ {n \ geq 2} $是同构（在某种意义上），然后$（t（w），δ）\ in \ in \ {（t（v），\ partial）\} $。
Let $R$ be a (P.I.D) and let $T(V),\partial)$ be a free $R$-dga. The quasi-isomorphism type of $(T(V),\partial)$ is the set, denoted $\{(T(V),\partial)\}$, of all free dgas which are quasi-isomorphic to $(T(V),\partial)$. In this paper we investigate to characterize and to compute the set $\{(T(V),\partial)\}$ for a new class of free dgas called perfect (a special kind of a perfect dga is the Adams-Hilton model of simply connected CW-complex such that $H_{*}(X,R)$ is free). We show that if $(T(V),\partial)$ and $(T(W),δ)$ are two perfect dgas, then $(T(W),δ)\in \{(T(V),\partial)\}$ if and only if their Whitehead exact sequences are isomorphic. Moreover we show that every dga $(T(V),\partial)$ can be split to give a pair $\big((T(V),\widetilde{\partial}),(π_{n})_{n\geq 2}\big)$ consisting with a perfect dga $(T(V),\widetilde{\partial})$ and a family of extensions $(π_{n})_{n\geq 2}$ and we establish that if $(T(W),\widetildeδ)\in \{(T(V),\widetilde{\partial})\}$ and if the extensions $(π_{n})_{n\geq 2}$ and $(π'_{n})_{n\geq 2}$ are isomorphic (in a certain sense), then $(T(W),δ)\in \{(T(V),\partial)\}$.
