论文标题
Stolz-Teichner计划中的电源操作
Power operations in the Stolz--Teichner program
论文作者
论文摘要
Stolz - Teichner计划提出了几何田地理论与某些共同体理论之间的深厚联系。在本文中，我们通过开发一种仅限于封闭界限的几何田地理论的几何能力操作理论扩展了这一联系。这些操作满足了类似于其同位物体表现的关系。我们还提供了计算工具，以识别几何定义的操作，并在复杂的Equivariant $ k $ - 理论上使用通常的功率操作。此外，我们使用几何方法来构建功率操作，以进行复杂性的椭圆形共同体。
The Stolz--Teichner program proposes a deep connection between geometric field theories and certain cohomology theories. In this paper, we extend this connection by developing a theory of geometric power operations for geometric field theories restricted to closed bordisms. These operations satisfy relations analogous to the ones exhibited by their homotopical counterparts. We also provide computational tools to identify the geometrically defined operations with the usual power operations on complexified equivariant $K$-theory. Further, we use the geometric approach to construct power operations for complexified equivariant elliptic cohomology.
