有限型曲面和对合曲面的对角复形
Diagonal complexes for surfaces of finite type and surfaces with involution
摘要：
研究了两个相关的构造：（1）对角复$\mathcal{D}$及其重心重分$\mathcal{BD}$与一个带有若干标记点的面向\textit{punctured}的曲面$F$有关。(2)对称对角复形$\mathcal{D}^{inv}$及其重心重分$\mathcal{BD}^{inv}$与对称（=对合）定向曲面$F$有关，曲面上有许多（对称放置的）标记点。消除一个穿刺会产生一个纤维束，其纤维与表面$F$的外科手术同胚。该束可以看作是“带孔的万有曲线”。的对称复杂的同伦等价于复杂的穿孔表面获得的手术的初始对称表面。
英文摘要：
Two related constructions are studied: (1) The diagonal complex $\mathcal{D}$ and its barycentric subdivision $\mathcal{BD}$ related to a \textit{punctured} oriented surface $F$ equipped with a number of labeled marked points. (2) The symmetric diagonal complex $\mathcal{D}^{inv}$ and its barycentric subdivision $\mathcal{BD}^{inv}$ related to a symmetric (=with an involution) oriented surface $F$ equipped with a number of (symmetrically placed) labeled marked points. Eliminating a puncture gives rise to a bundle whose fibers are homeomorphic to a surgery of the surface $F$. The bundle can be viewed as the "universal curve with holes". The symmetric complex is shown to be homotopy equivalent to the complex of a punctured surface obtained by a surgery of the initial symmetric surface.
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