111 citations · 386 across the 32 of their papers we have counts for
42 papers · 1 filter
Heegaard Floer knot trace invariants, exotic 4-manifolds, and symplectic obstructions
Jennifer Hom, Shunyu Wan
We show that the numerical invariants and coming from knot Floer homology are knot -trace invariants for any integer , resolving the remaining case in Hay…
Ribbon concordance and cabling
Jennifer Hom, JungHwan Park
We study ribbon concordances to cable knots. We formulate a conjecture predicting that any nontrivial knot admitting a ribbon concordance to a (p,q)-cable must itself be a (p,q)-ca…
Distinguishing exotic 's with Heegaard Floer homology
Sean Eli, Jennifer Hom, Tye Lidman
Attaching a Casson handle to a slice disk complement yields a smooth 4-manifold that is homeomorphic to . We show that if two slice knots have sufficiently different…
Topologically and rationally slice knots
Jennifer Hom, Sungkyung Kang, JungHwan Park
A knot in is topologically slice if it bounds a locally flat disk in . A knot in is rationally slice if it bounds a smooth disk in a rational homology ball. We pro…
PL-genus of surfaces in homology balls
Jennifer Hom, Matthew Stoffregen, Hugo Zhou
We consider manifold-knot pairs where is a homology sphere that bounds a homology ball. We show that the minimum genus of a PL surface in a homology ball such t…
Handle decomposition complexity and representation spaces
Paolo Aceto, Aliakbar Daemi, Jennifer Hom +2
We prove that there are homology three-spheres that bound definite four-manifolds, but any such bounding four-manifold must be built out of many handles. The argument uses the homo…
Unknotting number and cabling
Jennifer Hom, Tye Lidman, JungHwan Park
The unknotting number of knots is a difficult quantity to compute, and even its behavior under basic satelliting operations is not understood. We establish a lower bound on the unk…
An involutive dual knot surgery formula
Kristen Hendricks, Jennifer Hom, Matthew Stoffregen +1
We prove an involutive analog of the dual knot surgery formula of Eftekhary and Hedden-Levine. We also compute a small model for the local equivalence class of the involutive dual…
Naturality and functoriality in involutive Heegaard Floer homology
Kristen Hendricks, Jennifer Hom, Matthew Stoffregen +1
We prove first-order naturality of involutive Heegaard Floer homology, and furthermore construct well-defined maps on involutive Heegaard Floer homology associated to cobordisms be…
Homology concordance and knot Floer homology
Irving Dai, Jennifer Hom, Matthew Stoffregen +1
We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite numb…
Homology cobordism, knot concordance, and Heegaard Floer homology
Jennifer Hom
We review some recent results in knot concordance and homology cobordism. The proofs rely on various forms of Heegaard Floer homology. We also discuss related open problems.
Getting a handle on the Conway knot
Jennifer Hom
A knot is said to be slice if it bounds a smooth disk in the 4-ball. For 50 years, it was unknown whether a certain 11 crossing knot, called the Conway knot, was slice or not, and…
A note on PL-disks and rationally slice knots
Kristen Hendricks, Jennifer Hom, Matthew Stoffregen +1
We give infinitely many examples of manifold-knot pairs (Y, J) such that Y bounds an integer homology ball, J does not bound a non-locally-flat PL-disk in any integer homology ball…
On the quotient of the homology cobordism group by Seifert spaces
Kristen Hendricks, Jennifer Hom, Matthew Stoffregen +1
We prove that the quotient of the integer homology cobordism group by the subgroup generated by the Seifert fibered spaces is infinitely generated.
Linear independence of rationally slice knots
Jennifer Hom, Sungkyung Kang, JungHwan Park +1
A knot in is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot…
Surgery exact triangles in involutive Heegaard Floer homology
Kristen Hendricks, Jennifer Hom, Matthew Stoffregen +1
We establish a surgery exact triangle for involutive Heegaard Floer homology by using a doubling model of the involution. We use this exact triangle to give an involutive version o…
Lectures notes on Heegaard Floer homology
Jennifer Hom
These are the lecture notes for a course on Heegaard Floer homology held at PCMI in Summer 2019. We describe Heegaard diagrams, Heegaard Floer homology, knot Floer homology, and th…
Dehn surgery and non-separating two-spheres
Jennifer Hom, Tye Lidman
When can surgery on a null-homologous knot K in a rational homology sphere produce a non-separating sphere? We use Heegaard Floer homology to give sufficient conditions for K to be…
Ribbon knots, cabling, and handle decompositions
Jennifer Hom, Sungkyung Kang, JungHwan Park
The fusion number of a ribbon knot is the minimal number of 1-handles needed to construct a ribbon disk. The strong homotopy fusion number of a ribbon knot is the minimal number of…
More concordance homomorphisms from knot Floer homology
Irving Dai, Jennifer Hom, Matthew Stoffregen +1
We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence cla…
An infinite-rank summand of the homology cobordism group
Irving Dai, Jennifer Hom, Matthew Stoffregen +1
We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a $\mathbb{Z}^\infty…
Applications of involutive Heegaard Floer homology
Kristen Hendricks, Jennifer Hom, Tye Lidman
We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology…
Knot concordance in homology cobordisms
Jennifer Hom, Adam Simon Levine, Tye Lidman
Let denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a ques…
A note on knot concordance and involutive knot Floer homology
Kristen Hendricks, Jennifer Hom
We prove that if two knots are concordant, their involutive knot Floer complexes satisfy a certain type of stable equivalence.