A generalization of manifolds with corners
type: Item
instance of: scholarly article
title: A generalization of manifolds with corners
zbMATH Open document ID: 1359.58001
published in: Advances in Mathematics
publication date: 2016-07-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1501.00401
review text: In this paper the author introduces an extension of manifolds with corners, which he calls \textit{manifolds with generalized corners}, or just \textit{manifolds with \(g\)-corners}. The motivation for introducing these manifolds comes from potential applications in symplectic geometry. The definition is technical. A manifold with \(g\)-corners is a differential-geometric space locally modelled on the monoid \(X_P =\mathrm{Hom}_{\mathrm{Mon}}(P,[0,\infty))\) of morphisms of a weakly toric monoid \(P\) into the monoid \([0,\infty)\). In the case of the monoid \(P= {\mathbb N}^k\times {\mathbb Z}^{n-k}\), the monoid \(X_P\) is isomorphic to \([0,\infty)^k \times {\mathbb R}^{n-k}\), so that in this case we get the class of manifolds with corners. The paper is by nature rather technical but the notions are carefully introduced and explained.
reviewed by: Vagn Lundsgaard Hansen
Mathematics Subject Classification ID: 58A05
Mathematics Subject Classification ID: 57P99
zbMATH DE Number: 6604666
zbMATH Keywords: differential geometry
zbMATH Keywords: manifold with corners
zbMATH Keywords: boundary
zbMATH Keywords: monoid
zbMATH Keywords: category
zbMATH Keywords: transverse fibre product
zbMATH Keywords: Kuranishi space
author: Dominic Joyce
MaRDI profile type: Publication
OpenAlex ID: W2964325357
arXiv ID: 1501.00401
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DOI: 10.1016/J.AIM.2016.06.004
description: scientific article