Contractibility of boundaries of cocompact convex sets and embeddings of limit sets
We provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0){\rm{CAT}}\left(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively curved manifold group is “wild” in the boundary. Th...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-12-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.1515/agms-2024-0015 |
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| _version_ | 1846129288102805504 |
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| author | Bregman Corey Incerti-Medici Merlin |
| author_facet | Bregman Corey Incerti-Medici Merlin |
| author_sort | Bregman Corey |
| collection | DOAJ |
| description | We provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0){\rm{CAT}}\left(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively curved manifold group is “wild” in the boundary. The proof is based on a notion of coarse upper curvature bounds in terms of barycenters and the careful study of interpolation in geodesic metric spaces. |
| format | Article |
| id | doaj-art-fe3914b15c0648acb8e93f5619546a55 |
| institution | Kabale University |
| issn | 2299-3274 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj-art-fe3914b15c0648acb8e93f5619546a552024-12-10T07:29:34ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742024-12-01121pp. 8810910.1515/agms-2024-0015Contractibility of boundaries of cocompact convex sets and embeddings of limit setsBregman Corey0Incerti-Medici Merlin1Department of Mathematics, Tufts University, Medford, MA 02155, United States of AmericaFakultät für Mathematik, Universität Wien, 1090 Wien, AustriaWe provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0){\rm{CAT}}\left(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively curved manifold group is “wild” in the boundary. The proof is based on a notion of coarse upper curvature bounds in terms of barycenters and the careful study of interpolation in geodesic metric spaces.https://doi.org/10.1515/agms-2024-0015cat(0) spacescartan-hadamard manifoldbarycenterscontractibilityquasi-convex codimension one subgroups53c2352a20 (primary)51f3020f6520f67 (secondary) |
| spellingShingle | Bregman Corey Incerti-Medici Merlin Contractibility of boundaries of cocompact convex sets and embeddings of limit sets Analysis and Geometry in Metric Spaces cat(0) spaces cartan-hadamard manifold barycenters contractibility quasi-convex codimension one subgroups 53c23 52a20 (primary) 51f30 20f65 20f67 (secondary) |
| title | Contractibility of boundaries of cocompact convex sets and embeddings of limit sets |
| title_full | Contractibility of boundaries of cocompact convex sets and embeddings of limit sets |
| title_fullStr | Contractibility of boundaries of cocompact convex sets and embeddings of limit sets |
| title_full_unstemmed | Contractibility of boundaries of cocompact convex sets and embeddings of limit sets |
| title_short | Contractibility of boundaries of cocompact convex sets and embeddings of limit sets |
| title_sort | contractibility of boundaries of cocompact convex sets and embeddings of limit sets |
| topic | cat(0) spaces cartan-hadamard manifold barycenters contractibility quasi-convex codimension one subgroups 53c23 52a20 (primary) 51f30 20f65 20f67 (secondary) |
| url | https://doi.org/10.1515/agms-2024-0015 |
| work_keys_str_mv | AT bregmancorey contractibilityofboundariesofcocompactconvexsetsandembeddingsoflimitsets AT incertimedicimerlin contractibilityofboundariesofcocompactconvexsetsandembeddingsoflimitsets |