Smooth Singular Cubes

Will J. Merry
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Will J. Merry: ETH Zürich, Departement Mathematik

Chapter Chapter 25 in Lectures on Differential Geometry I, 2026, pp 255-261 from Springer

Abstract: Abstract In this chapter we begin our discussion of integration on manifolds. We introduce the notion of a singular cube in a manifold and explain how a differential form can be integrated over such a cube. We then mirror the construction of singular homology and show how to create the (smooth) cubical chain complex of M. We will use this formalism next chapter en route to proving the manifold version of Stokes’ Theorem.

Date: 2026
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DOI: 10.1007/978-3-032-03733-6_25

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