瑞士奶酪店
The Swiss-Cheese Operad
摘要：
我们引入一个新的操作，我们称之为瑞士奶酪操作。它自然地混合了小圆盘和小音程操作。瑞士奶酪操作与上半平面上的点和实直线上的点的位形空间有关，孔采维奇为了变形量子化而考虑了这一点。这种关系类似于小圆盘操作数与平面上点的位形空间之间的关系。瑞士奶酪操作数也可以看作是Zwiebach最近研究的开闭弦理论中出现的亏格为零的黎曼曲面的模空间的有限维模型。我们描述代数上的瑞士奶酪操作的同源性。
英文摘要：
We introduce a new operad, which we call the Swiss-cheese operad. It mixes naturally the little disks and the little intervals operads. The Swiss-cheese operad is related to the configuration spaces of points on the upper half-plane and points on the real line, considered by Kontsevich for the sake of deformation quantization. This relation is similar to the relation between the little disks operad and the configuration spaces of points on the plane. The Swiss-cheese operad may also be regarded as a finite-dimensional model of the moduli space of genus-zero Riemann surfaces appearing in the open-closed string theory studied recently by Zwiebach. We describe algebras over the homology of the Swiss-cheese operad.
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