论文标题
关于戈伦斯坦空间的拓扑复杂性
On Topological Complexity of Gorenstein spaces
论文作者
论文摘要
在本文中，使用Sullivan的简单连接有限类型CW复合物的理性同义理论，我们赋予了$ \ Mathbb {q} $ - 向量空间$ \ MATHCAL {E} XT_ {C^{\ AST}（X; \ Mathbb {Q}）}（\ Mathbb {Q}，C^{\ ast}（x; \ Mathbb {q} Q}））$，具有渐变的通勤Algebra结构。这导致我们引入了$ \ Mathcal {e} XT $ - $ x_0 $的高级（分别模块，同源性）拓扑复杂性，$ x $的合理化（$ x $ of $ x $ over $ \ mathbb {q} $）。然后，我们对这些不变的及其在戈伦斯坦空间各自的普通次数进行比较。在这种情况下，我们还强调了亚当斯·希尔顿（Adams-Hilton）模型比奇数特征的益处，尤其是在两个情况下，第一个案例是$ 2 $ -CELL CW-COMPERX，而第二个则是悬架。
In this paper, using Sullivan's approach to rational homotopy theory of simply-connected finite type CW complexes, we endow the $\mathbb{Q}$-vector space $\mathcal{E}xt_{C^{\ast}(X;\mathbb{Q})}(\mathbb{Q},C^{\ast}(X;\mathbb{Q}))$ with a graded commutative algebra structure. This leads us to introduce the $\mathcal{E}xt$-version of higher (resp. module, homology) topological complexity of $X_0$, the rationalization of $X$ (resp. of $X$ over $\mathbb{Q}$). We then make comparisons between these invariants and their respective ordinary ones for Gorenstein spaces. We also highlight, in this context, the benefit of Adams-Hilton models over a field of odd characteristics especially through two cases, the first one when the space is a $2$-cell CW-complex and the second one when it is a suspension.
