{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1241"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1241","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"On the geometry and topology of moduli spaces of multi-polygonal linkages","abstract":"The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact algebraic varieties. Multi-quadrilateral linkages whose moduli spaces are at most one dimensional are classified. The dimensions and some Euler characteristics are computed, and conditions under which these spaces are smooth manifolds are determined. Some conditions are also given for when the moduli spaces are connected and when they are disjoint unions of two moduli spaces of polygonal linkages.","abstract_html":"The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact algebraic varieties. Multi-quadrilateral linkages whose moduli spaces are at most one dimensional are classified. The dimensions and some Euler characteristics are computed, and conditions under which these spaces are smooth manifolds are determined. Some conditions are also given for when the moduli spaces are connected and when they are disjoint unions of two moduli spaces of polygonal linkages.","abstract_has_math":false,"creators":["Holcomb, Michael Edward"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-01-01T08:00:00Z","date_published":"2003-01-01T08:00:00Z","updated_at":"2026-07-24T02:57:21Z","subjects":["topology","moduli","linkages"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-0409103-153131","https://repository.lsu.edu/gradschool_dissertations/242"],"render_values":[{"text":"etd-0409103-153131","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/242","href":"https://repository.lsu.edu/gradschool_dissertations/242","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.242","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Holcomb, Michael Edward"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2003-03-31"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:08:10Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["topology","moduli","linkages"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-0409103-153131","10.31390/gradschool_dissertations.242","https://repository.lsu.edu/gradschool_dissertations/242"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact algebraic varieties. Multi-quadrilateral linkages whose moduli spaces are at most one dimensional are classified. The dimensions and some Euler characteristics are computed, and conditions under which these spaces are smooth manifolds are determined. Some conditions are also given for when the moduli spaces are connected and when they are disjoint unions of two moduli spaces of polygonal linkages."]},{"key":"dc:title","label":"Title","values":["On the geometry and topology of moduli spaces of multi-polygonal linkages"]}]}],"canonical_facts":{"dc:creator":["Holcomb, Michael Edward"],"dc:date":["2003-03-31"],"dc:date.available":["2022-05-12T23:08:10Z"],"dc:description.abstract":["The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact algebraic varieties. Multi-quadrilateral linkages whose moduli spaces are at most one dimensional are classified. The dimensions and some Euler characteristics are computed, and conditions under which these spaces are smooth manifolds are determined. Some conditions are also given for when the moduli spaces are connected and when they are disjoint unions of two moduli spaces of polygonal linkages."],"dc:identifier":["etd-0409103-153131","10.31390/gradschool_dissertations.242","https://repository.lsu.edu/gradschool_dissertations/242"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["topology","moduli","linkages"],"dc:title":["On the geometry and topology of moduli spaces of multi-polygonal linkages"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:57:21Z"}