A generalization of manifolds with corners
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.
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