Path space connections and categorical geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:75

Article

Chatterjee, Saikat¹  Lahiri, Amitabha²  Sengupta, Ambar N.³ 

[1] Inst Math Sci, Dept Math, Madras 600113, Tamil Nadu, India

[2] SN Bose Natl Ctr Basic Sci, Kolkata 700098, W Bengal, India

[3] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

关键词: Bundles;    Connections;    Path spaces;    Category theory;   

DOI  :  10.1016/j.geomphys.2013.09.006

来源: Elsevier

【 摘 要 】

We develop a new differential geometric structure using category theoretic tools that provides a powerful framework for studying bundles over path spaces. We study a type of connection forms, given by Chen integrals, over path spaces by placing such forms within a category-theoretic framework of principal bundles and connections. A new notion of 'decorated' principal bundles is introduced, along with parallel transport for such bundles, and specific examples in the context of path spaces are developed. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free