We use the functoriality of Khovanov homology to examine the smooth, boundary-preserving isotopy of surfaces embedded in the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on Khovanov homology. Similar techniques produce an infinite family of knots that each bound a pair of exotic surfaces of arbitrary genus.
","abstract_html":"<p>We use the functoriality of Khovanov homology to examine the smooth, boundary-preserving isotopy of surfaces embedded in the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on Khovanov homology. Similar techniques produce an infinite family of knots that each bound a pair of exotic surfaces of arbitrary genus.</p>","abstract_has_math":false,"creators":["Sundberg, Isaac"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Open Access","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-01-01T08:00:00Z","date_published":"2022-01-01T08:00:00Z","updated_at":"2026-07-24T01:23:53Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.brynmawr.edu/dissertations/225","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Sundberg, Isaac"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://repository.brynmawr.edu/dissertations/225"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We use the functoriality of Khovanov homology to examine the smooth, boundary-preserving isotopy of surfaces embedded in the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on Khovanov homology. Similar techniques produce an infinite family of knots that each bound a pair of exotic surfaces of arbitrary genus.
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