{"id":{"repo_id":"duke","oai_identifier":"oai:dukespace.lib.duke.edu:10161/25199"},"canonical_url":"https://search.dev.ndltd.org/etd/duke/oai:dukespace.lib.duke.edu:10161/25199","repository":{"repo_id":"duke","name":"Duke University","base_url":"https://dukespace.lib.duke.edu/server/oai/request"},"display":{"title":"Invariance of Knot Lattice Homology and Homotopy","abstract":"<p>Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice homology is an invariant of the smooth knot type of a generalized algebraic knot in a rational homology sphere. In that case, knot lattice homology can be realized as the cellular homology of a doubly-filtered homotopy type, which is itself invariant. Along the way, we show that the topological link type of a generalized algebraic link determines the nested singularity type. </p>","abstract_html":"&lt;p&gt;Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice homology is an invariant of the smooth knot type of a generalized algebraic knot in a rational homology sphere. In that case, knot lattice homology can be realized as the cellular homology of a doubly-filtered homotopy type, which is itself invariant. Along the way, we show that the topological link type of a generalized algebraic link determines the nested singularity type. &lt;/p&gt;","abstract_has_math":false,"creators":["Niemi-Colvin, Seppo Matthew"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Levine, Adam"],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022","date_published":"2022","updated_at":"2026-07-24T02:07:01Z","subjects":["Mathematics","knot Floer homology","knot theory","singularity theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10161/25199","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Levine, Adam"]},{"key":"dc:creator","label":"Author","values":["Niemi-Colvin, Seppo Matthew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-06-15T18:43:12Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-06-15T18:43:12Z"]},{"key":"dc:date.issued","label":"Date","values":["2022"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","knot Floer homology","knot theory","singularity theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10161/25199"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice homology is an invariant of the smooth knot type of a generalized algebraic knot in a rational homology sphere. In that case, knot lattice homology can be realized as the cellular homology of a doubly-filtered homotopy type, which is itself invariant. Along the way, we show that the topological link type of a generalized algebraic link determines the nested singularity type. </p>"]},{"key":"dc:title","label":"Title","values":["Invariance of Knot Lattice Homology and Homotopy"]}]}],"canonical_facts":{"dc:contributor.advisor":["Levine, Adam"],"dc:creator":["Niemi-Colvin, Seppo Matthew"],"dc:date.accessioned":["2022-06-15T18:43:12Z"],"dc:date.available":["2022-06-15T18:43:12Z"],"dc:date.issued":["2022"],"dc:description.abstract":["<p>Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice homology is an invariant of the smooth knot type of a generalized algebraic knot in a rational homology sphere. In that case, knot lattice homology can be realized as the cellular homology of a doubly-filtered homotopy type, which is itself invariant. Along the way, we show that the topological link type of a generalized algebraic link determines the nested singularity type. </p>"],"dc:identifier.uri":["https://hdl.handle.net/10161/25199"],"dc:subject":["Mathematics","knot Floer homology","knot theory","singularity theory"],"dc:title":["Invariance of Knot Lattice Homology and Homotopy"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:07:01Z"}