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IBS - CGP SeminarㅣSome results and conjectures the rank of some knot homologies

기간 : 2022-12-15 ~ 2022-12-15
시간 : 17:00 ~ 18:00
개최 장소 : Online streaming (Zoom)
분야Field
날짜Date 2022-12-15 ~ 2022-12-15 시간Time 17:00 ~ 18:00
장소Place Online streaming (Zoom) 초청자Host
연사Speaker Marco Marengon 소속Affiliation Alfréd Rényi Institute for Mathematics
TOPIC IBS - CGP SeminarㅣSome results and conjectures the rank of some knot homologies
소개 및 안내사항Content

Some results and conjectures the rank of some knot homologies 

Given a knot in the 3-sphere, one can associate some knot homologies with it, among which knot Floer homology and (reduced) Khovanov homology. Motivated by Fox-Milnor's obstruction for slice knots, we prove that all knots in a certain family have these homologies with total rank being a square integer. Moreover, we conjecture that the rank of knot Floer homology is congruent to 1 modulo 8 for all slice knots, and we prove this fact for a subfamily of slice knots, namely fusion number 1 ribbon knots. This is a joint work with Hockenhull and Willis, and partially also with Dunfield and Gong. 

Pre-registration is certainly required, please visit https://cgp.ibs.re.kr/ 

 

학회명Field IBS - CGP SeminarㅣSome results and conjectures the rank of some knot homologies
날짜Date 2022-12-15 ~ 2022-12-15 시간Time 17:00 ~ 18:00
장소Place Online streaming (Zoom) 초청자Host
소개 및 안내사항Content

Some results and conjectures the rank of some knot homologies 

Given a knot in the 3-sphere, one can associate some knot homologies with it, among which knot Floer homology and (reduced) Khovanov homology. Motivated by Fox-Milnor's obstruction for slice knots, we prove that all knots in a certain family have these homologies with total rank being a square integer. Moreover, we conjecture that the rank of knot Floer homology is congruent to 1 modulo 8 for all slice knots, and we prove this fact for a subfamily of slice knots, namely fusion number 1 ribbon knots. This is a joint work with Hockenhull and Willis, and partially also with Dunfield and Gong. 

Pre-registration is certainly required, please visit https://cgp.ibs.re.kr/ 

 

성명Field IBS - CGP SeminarㅣSome results and conjectures the rank of some knot homologies
날짜Date 2022-12-15 ~ 2022-12-15 시간Time 17:00 ~ 18:00
소속Affiliation Alfréd Rényi Institute for Mathematics 초청자Host
소개 및 안내사항Content

Some results and conjectures the rank of some knot homologies 

Given a knot in the 3-sphere, one can associate some knot homologies with it, among which knot Floer homology and (reduced) Khovanov homology. Motivated by Fox-Milnor's obstruction for slice knots, we prove that all knots in a certain family have these homologies with total rank being a square integer. Moreover, we conjecture that the rank of knot Floer homology is congruent to 1 modulo 8 for all slice knots, and we prove this fact for a subfamily of slice knots, namely fusion number 1 ribbon knots. This is a joint work with Hockenhull and Willis, and partially also with Dunfield and Gong. 

Pre-registration is certainly required, please visit https://cgp.ibs.re.kr/ 

 

성명Field IBS - CGP SeminarㅣSome results and conjectures the rank of some knot homologies
날짜Date 2022-12-15 ~ 2022-12-15 시간Time 17:00 ~ 18:00
호실Host 인원수Affiliation Marco Marengon
사용목적Affiliation 신청방식Host Alfréd Rényi Institute for Mathematics
소개 및 안내사항Content

Some results and conjectures the rank of some knot homologies 

Given a knot in the 3-sphere, one can associate some knot homologies with it, among which knot Floer homology and (reduced) Khovanov homology. Motivated by Fox-Milnor's obstruction for slice knots, we prove that all knots in a certain family have these homologies with total rank being a square integer. Moreover, we conjecture that the rank of knot Floer homology is congruent to 1 modulo 8 for all slice knots, and we prove this fact for a subfamily of slice knots, namely fusion number 1 ribbon knots. This is a joint work with Hockenhull and Willis, and partially also with Dunfield and Gong. 

Pre-registration is certainly required, please visit https://cgp.ibs.re.kr/ 

 

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