On manifolds with corners
By D. Joyce. 2009
158 citations recorded by the source corpus.
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind. We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y. Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c. Our theory is tailored to future applications in Symplectic Geometry, and is part of a project to describe the geometric structure on moduli spaces of J-holomorphic curves in a new way. But we have written it as a separate paper as we believe it is of independent interest.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5d766741ead564a9df0965e4b36f291b02cf31bd
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Tame topology of arithmetic quotients and algebraicity of Hodge loci (2018, background): “This is a real-analytic n -manifold with corners for n > 0, endowed with an immersion (not necessarily injective) i X : ∂X −→ X (cf. [Joy12, prop.2.7]) which is real-analytic ([Joy12, Theor.”
- A generalization of manifolds with corners (2015, background): “7], Kottke and Melrose [18], Margalef-Roig and Outerelo Dominguez [20], Melrose [24–26], Monthubert [27], and the author [9], [10, §5].”
- Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, background): “In this way the branch cut I plays the role of a “corner” separating Σ3 into regions [50].”