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UID:4010b4eed0869bf8099ebf82e4028104
CATEGORIES:Topology/Geometry Seminar
CREATED:20230213T122240
SUMMARY:Whitehead doubles, Conway tangles and rank-expansion
LOCATION:Hill Center\, Room 705
DESCRIPTION:<p>Seminar website:&nbsp;<a href="https://sites.google.com/view/rutgersgeom
 etrytopologyseminar/home">https://sites.google.com/view/rutgersgeometrytopo
 logyseminar/home</a></p>
CONTACT:Abhishek Mallick (Rutgers University-New Brunswick)
X-EXTRAINFO:Abstract:\nHedden and Pinzón-Caicedo conjectured that every non-constant, w
 inding number zero, satellite operation on the knot concordance group must 
 admit an extreme form of rank-expansion, namely they map a rank-one subgrou
 p to an infinite rank subgroup. In this talk, we will give the first known 
 example of such a phenomenon by showing that the Whitehead doubles admit su
 ch a behavior, answering a question posed by Hedden and Pinzón-Caicedo. In 
 fact, we will show that the conjecture holds for a larger class of satellit
 e knots defined using Conway tangles. We will also recover many existing re
 sults on rank-conservation in the literature proved using gauge theoretic m
 ethods. Our primary tool is a surgery formula in Heegaard Floer homology pr
 oved by Hendricks-Hom-Stoffregen and Zemke. This is joint work with Irving 
 Dai, Matt Hedden and Matt Stoffregen. 
DTSTAMP:20260924T041032
DTSTART;TZID=America/New_York:20230214T160000
DTEND;TZID=America/New_York:20230214T170000
SEQUENCE:0
TRANSP:OPAQUE
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