复曲面类
Toric Genera
摘要：
我们的主要目的是发展一个理论的等变一般的稳定复流形配备兼容行动的环面T^k。在全向拟流形的情况下，我们提出的计算，只依赖于他们定义的组合数据，这些灵感来自类似的计算在环面几何，试图表达算术，椭圆，和相关的属环面品种的条款，只有他们的球迷。我们的理论集中在泛环面亏格Φ上，它是由Krichever和Loeffler在1974年独立引入的，尽管从根本上不同的观点。事实上Φ是汤姆·迪克1970年的捆绑变换的一个版本，定义在T^k-等变复配边类上，取值于分类空间的复配边代数。我们继续结合分析，形式群理论，同伦方法的属，并提到指数理论的方法作为一个经常性的洞察力和动机的来源。由此产生的灵活性，使我们能够在我们的框架内确定几个不同的属，并引入参数化的版本，适用于束配备了一个稳定的复结构的切线沿其纤维。在孤立的不动点的存在下，我们得到了普遍的局部化公式，其应用包括识别Krichever的广义椭圆属之间的通用属是刚性的SU-流形。我们遵循复曲面几何的传统，尽可能使用各种说明性示例。作为背景和前提，我们试图调和自20世纪60年代以来独立发展了几十年的东西方文学。
英文摘要：
Our primary aim is to develop a theory of equivariant genera for stably complex manifolds equipped with compatible actions of a torus T^k. In the case of omnioriented quasitoric manifolds, we present computations that depend only on their defining combinatorial data; these draw inspiration from analogous calculations in toric geometry, which seek to express arithmetic, elliptic, and associated genera of toric varieties in terms only of their fans. Our theory focuses on the universal toric genus Φ, which was introduced independently by Krichever and Loeffler in 1974, albeit from radically different viewpoints. In fact Φis a version of tom Dieck's bundling transformation of 1970, defined on T^k-equivariant complex cobordism classes and taking values in the complex cobordism algebra of the classifying space. We proceed by combining the analytic, the formal group theoretic, and the homotopical approaches to genera, and refer to the index theoretic approach as a recurring source of insight and motivation. The resultant flexibility allows us to identify several distinct genera within our framework, and to introduce parametrised versions that apply to bundles equipped with a stably complex structure on the tangents along their fibres. In the presence of isolated fixed points, we obtain universal localisation formulae, whose applications include the identification of Krichever's generalised elliptic genus as universal amongst genera that are rigid on SU-manifolds. We follow the traditions of toric geometry by working with a variety of illustrative examples wherever possible. For background and prerequisites we attempt to reconcile the literature of east and west, which developed independently for several decades after the 1960s.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
