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Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams

Abstract:

The diameter of a disc filling a loop in the universal covering of a Riemannian manifold may be measured extrinsically using the distance function on the ambient space or intrinsically using the induced length metric on the disc. Correspondingly, the diameter of a van Kampen diagram filling a word that represents the identity in a finitely presented group can either be measured intrinsically its 1-skeleton or extrinsically in the Cayley graph of the group. We construct the first examples of c...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
Journal of Differential Geometry, 82(1), 115-154, 2009
Publication date:
2005-10-31
URN:
uuid:ba934e0c-4ff6-46c8-a53f-49820ff596de
Source identifiers:
146969
Local pid:
pubs:146969

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