کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6425212 | 1633789 | 2016 | 103 صفحه PDF | دانلود رایگان |
In conventional Differential Geometry one studies manifolds, locally modelled on Rn, manifolds with boundary, locally modelled on [0,â)ÃRnâ1, and manifolds with corners, locally modelled on [0,â)kÃRnâk. They form categories ManâManbâManc. Manifolds with corners X have boundaries âX, also manifolds with corners, with dimâX=dimXâ1.We introduce a new notion of manifolds with generalized corners, or manifolds with g-corners, extending manifolds with corners, which form a category Mangc with ManâManbâMancâMangc. Manifolds with g-corners are locally modelled on XP=HomMon(P,[0,â)) for P a weakly toric monoid, where XPâ [0,â)kÃRnâk for P=NkÃZnâk.Most differential geometry of manifolds with corners extends nicely to manifolds with g-corners, including well-behaved boundaries âX. In some ways manifolds with g-corners have better properties than manifolds with corners; in particular, transverse fibre products in Mangc exist under much weaker conditions than in Manc.This paper was motivated by future applications in symplectic geometry, in which some moduli spaces of J-holomorphic curves can be manifolds or Kuranishi spaces with g-corners rather than ordinary corners.Our manifolds with g-corners are related to the 'interior binomial varieties' of Kottke and Melrose [20], and the 'positive log differentiable spaces' of Gillam and Molcho [6].
Journal: Advances in Mathematics - Volume 299, 20 August 2016, Pages 760-862