{"id":{"repo_id":"anu","oai_identifier":"oai:openresearch-repository.anu.edu.au:1885/137198"},"canonical_url":"https://search.dev.ndltd.org/etd/anu/oai:openresearch-repository.anu.edu.au:1885/137198","repository":{"repo_id":"anu","name":"Australian National University","base_url":"https://openresearch-repository.anu.edu.au/server/oai/request"},"display":{"title":"A geometry theory of wild arcs","abstract":"A topological embedding of a I-cell in the 3-sphere is called an arc. Arcs which are wild at a single point have been the subject of a number of studies over the past twenty five years. They have proven to be interesting in their own right as well as being sources for examples of topological embeddings in 3-manifolds. This thesis is devoted to a characterization of arcs which are wild at a single point, at which they have finite penetration index, in terms of sequences of tame sets. In order to do this the notion of a \"prime\" arc is defined and a unique prime decomposition theorem is proved. The prime arcs have the property that \"levels\" of \"echelon neighbourhoods\", which are 3-cells surrounding the wild point, can be defined. The characterization involves studying these levels. If the penetration index is three the characterization becomes particularly easy and Chapter 6 is devoted to a description of arcs of penetration index three.","abstract_html":"A topological embedding of a I-cell in the 3-sphere is called an arc. Arcs which are wild at a single point have been the subject of a number of studies over the past twenty five years. They have proven to be interesting in their own right as well as being sources for examples of topological embeddings in 3-manifolds. This thesis is devoted to a characterization of arcs which are wild at a single point, at which they have finite penetration index, in terms of sequences of tame sets. In order to do this the notion of a "prime" arc is defined and a unique prime decomposition theorem is proved. The prime arcs have the property that "levels" of "echelon neighbourhoods", which are 3-cells surrounding the wild point, can be defined. The characterization involves studying these levels. If the penetration index is three the characterization becomes particularly easy and Chapter 6 is devoted to a description of arcs of penetration index three.","abstract_has_math":false,"creators":["Hemion, Geoffrey John"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1974,"date_issued":"1974","date_published":"1974","updated_at":"2026-07-24T00:54:54Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["b1016112"],"render_values":[{"text":"b1016112","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1885/137198","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hemion, Geoffrey John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-12-08T02:21:14Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-12-08T02:21:14Z"]},{"key":"dc:date.issued","label":"Date","values":["1974"]},{"key":"dc:type","label":"Dc Type","values":["Thesis (PhD)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["b1016112"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1885/137198"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A topological embedding of a I-cell in the 3-sphere is called an arc. Arcs which are wild at a single point have been the subject of a number of studies over the past twenty five years. They have proven to be interesting in their own right as well as being sources for examples of topological embeddings in 3-manifolds. This thesis is devoted to a characterization of arcs which are wild at a single point, at which they have finite penetration index, in terms of sequences of tame sets. In order to do this the notion of a \"prime\" arc is defined and a unique prime decomposition theorem is proved. The prime arcs have the property that \"levels\" of \"echelon neighbourhoods\", which are 3-cells surrounding the wild point, can be defined. The characterization involves studying these levels. If the penetration index is three the characterization becomes particularly easy and Chapter 6 is devoted to a description of arcs of penetration index three."]},{"key":"dc:title","label":"Title","values":["A geometry theory of wild arcs"]}]}],"canonical_facts":{"dc:creator":["Hemion, Geoffrey John"],"dc:date.accessioned":["2017-12-08T02:21:14Z"],"dc:date.available":["2017-12-08T02:21:14Z"],"dc:date.issued":["1974"],"dc:description.abstract":["A topological embedding of a I-cell in the 3-sphere is called an arc. Arcs which are wild at a single point have been the subject of a number of studies over the past twenty five years. They have proven to be interesting in their own right as well as being sources for examples of topological embeddings in 3-manifolds. This thesis is devoted to a characterization of arcs which are wild at a single point, at which they have finite penetration index, in terms of sequences of tame sets. In order to do this the notion of a \"prime\" arc is defined and a unique prime decomposition theorem is proved. The prime arcs have the property that \"levels\" of \"echelon neighbourhoods\", which are 3-cells surrounding the wild point, can be defined. The characterization involves studying these levels. If the penetration index is three the characterization becomes particularly easy and Chapter 6 is devoted to a description of arcs of penetration index three."],"dc:identifier.other":["b1016112"],"dc:identifier.uri":["http://hdl.handle.net/1885/137198"],"dc:language.iso":["en"],"dc:title":["A geometry theory of wild arcs"],"dc:type":["Thesis (PhD)"]},"updated_at":"2026-07-24T00:54:54Z"}