Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 2, pp. 369-381 (2008)

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Curvature in synthetic differential geometry of groupoids

Hirokazu Nishimura

Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan, e-mail:logic {\em at} math.tsukuba.ac.jp

Abstract: We study the fundamental properties of curvature in groupoids within the framework of synthetic differential geometry. As is usual in synthetic differential geometry, its combinatorial nature is emphasized. In particular, the classical Bianchi identity is deduced from a combinatorial version of it.

Keywords: Curvature, synthetic differential geometry, second Bianchi identity, combinatorial Bianchi identity, groupoids

Classification (MSC2000): 51K10

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Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.

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