扭曲微分k理论的几何模型I

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2017-05-13 DOI:10.1007/s40062-017-0177-z

Byungdo Park

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引用次数: 12

摘要

本文是构建扭曲微分k理论几何模型系列论文中的第一篇。当底层拓扑扭转表示一个扭转类时，我们构造了一个偶扭转微分k理论模型。微分扭转指的是带连接的光滑U(1)-gerbes，我们使用带连接的扭转矢量束作为环。我们构造的模型满足Kahle和Valentino公理，包括函数性、扭转的自然性和六边形图。本文证实了一个长期存在的假设，即带连接的扭曲向量束定义了扭曲微分k理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Geometric models of twisted differential K-theory I

This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. By differential twists we will mean smooth U(1)-gerbes with connection, and we use twisted vector bundles with connection as cocycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. This paper confirms a long-standing hypothetical idea that twisted vector bundles with connection define twisted differential K-theory.

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Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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