NDLI: Extended hyperbolicity

Content Provider	Springer Nature Link
Author	Tomassini, Giuseppe Borghesi, Simone
Copyright Year	2010
Abstract	The concept of Brody hyperbolicity is interpreted in terms of homotopy-theoretic structures. We extend the definition of Brody hyperbolicity to simplicial sheaves of sets over the site of complex spaces with the strong topology. Imitating one possible definition of homotopy groups for a topological space, we defined the holotopy groups for a simplicial sheaf and showed that their vanishing in “positive” degrees is a necessary condition for a sheaf to be Brody hyperbolic. A partial converse to this theorem is proved at the end of the paper. We deduce that if X is a complex space with a nonzero holotopy group in positive degree, then X cannot be weakly equivalent (in a particular sense) to a hyperbolic complex space (in particular is not itself hyperbolic). We finish the manuscript by applying these results along with a topological realization functor, constructed in the previous section, to prove that complex projective spaces cannot be weakly equivalent to hyperbolic complex spaces.
Ending Page	284
Page Count	24
Starting Page	261
File Format	PDF
ISSN	03733114
e-ISSN	16181891
Journal	Annali di Matematica Pura ed Applicata
Issue Number	2
Volume Number	191
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-12-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Kobayashi Hyperbolic spaces Simplicial sheaves Homotopical algebra Simplicial sets, simplicial objects (in a category) Mathematics Hyperbolic and Kobayashi hyperbolic manifolds
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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