Axiomatic Differential Geometry II-2: Differential Forms
Hirokazu Nishimura
TL;DR
This paper refines an axiomatic framework for differential geometry, focusing on the adaptation of differential forms within this setting to enhance theoretical understanding.
Contribution
It introduces an adapted theory of differential forms within a revised axiomatic differential geometry framework, building on previous foundational work.
Findings
A new axiomatic formulation of differential geometry.
An adapted theory of differential forms within the axiomatic framework.
Enhanced conceptual clarity of Euclideaness in differential geometry.
Abstract
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to our present axiomatic framework.
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Taxonomy
TopicsAdvanced Topics in Algebra · Mathematics and Applications · Homotopy and Cohomology in Algebraic Topology