Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams
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 t...
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| Format: | Journal article |
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International Press
2009
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| _version_ | 1797074987705696256 |
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| author | Bridson, M Riley, T |
| author_facet | Bridson, M Riley, T |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | 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 closed manifolds and finitely presented groups for which this choice -- intrinsic versus extrinsic -- gives rise to qualitatively different min-diameter filling functions. |
| first_indexed | 2024-03-06T23:44:03Z |
| format | Journal article |
| id | oxford-uuid:704a4abc-f04e-44d4-98a1-3598b19d0068 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:44:03Z |
| publishDate | 2009 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:704a4abc-f04e-44d4-98a1-3598b19d00682022-03-26T19:36:10ZExtrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagramsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:704a4abc-f04e-44d4-98a1-3598b19d0068Symplectic Elements at OxfordInternational Press2009Bridson, MRiley, TThe 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 closed manifolds and finitely presented groups for which this choice -- intrinsic versus extrinsic -- gives rise to qualitatively different min-diameter filling functions. |
| spellingShingle | Bridson, M Riley, T Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams |
| title | Extrinsic versus intrinsic diameter for Riemannian filling-discs and van
Kampen diagrams |
| title_full | Extrinsic versus intrinsic diameter for Riemannian filling-discs and van
Kampen diagrams |
| title_fullStr | Extrinsic versus intrinsic diameter for Riemannian filling-discs and van
Kampen diagrams |
| title_full_unstemmed | Extrinsic versus intrinsic diameter for Riemannian filling-discs and van
Kampen diagrams |
| title_short | Extrinsic versus intrinsic diameter for Riemannian filling-discs and van
Kampen diagrams |
| title_sort | extrinsic versus intrinsic diameter for riemannian filling discs and van kampen diagrams |
| work_keys_str_mv | AT bridsonm extrinsicversusintrinsicdiameterforriemannianfillingdiscsandvankampendiagrams AT rileyt extrinsicversusintrinsicdiameterforriemannianfillingdiscsandvankampendiagrams |