Heegaard Floer homology and splicing homology spheres

Cagri Karakurt; Eamonn Tweedy; Tye Lidman

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Heegaard Floer homology and splicing homology spheres

Cagri Karakurt, Tye Lidman, Eamonn Tweedy

Geometric Topology · Submitted 7 Apr 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove a basic inequality for the d-invariants of a splice of knots in homology spheres.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,999 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.86 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We prove a basic inequality for the d-invariants of a splice of knots in homology spheres. As a result, we are able to prove a new relation on the rank of reduced Floer homology under maps between Seifert fibered homology spheres, improving results of the first and second authors. As a corollary, a degree one map between two aspherical Seifert homology spheres is homotopic to a homeomorphism if and only if the Heegaard Floer homologies are isomorphic.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove a basic inequality for the d-invariants of a splice of knots in homology spheres.	result 0.71	0.96	0.62	asserted 1.00
s1	As a result, we are able to prove a new relation on the rank of reduced Floer homology under maps between Seifert fibered homology spheres, improving results of the first and second authors.	result 0.91	0.95	0.24	asserted 0.99
s2	As a corollary, a degree one map between two aspherical Seifert homology spheres is homotopic to a homeomorphism if and only if the Heegaard Floer homologies are isomorphic.	result 0.96	0.88	0.34	asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We prove a basic inequality for the d-invariants of a splice of knots in homology spheres. As a result, we are able to prove a new relation on the rank of reduced Floer homology under maps between Seifert fibered homology spheres, improving results of the first and second authors. As a corollary, a degree one map between two aspherical Seifert homology spheres is homotopic to a homeomorphism if and only if the Heegaard Floer homologies are isomorphic.

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3 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Uses its method or tool 1 paper

In particular, combining Theorem [ref] with techniques of [ref] one can compute $d$-invariants of large classes of graph homology spheres.

Ozsvath-Szabo $d$-invariants of almost simple linear graphs · Introduction · 0.89

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Compares with 1 paper

Then, [equation] This should be compared to the work of Hanselman-Rasmussen-Watson [ref] , who prove that $HF(Y) ≥HF(Y_i)$ for an arbitrary splice.

Bordered Floer homology for manifolds with torus boundary via immersed curves · Introduction · 1.00

Cites as background 1 paper

Recall that $d ≤d ≤d$ [ref] and that $HF_conn = 0$ if and only if $d = d$ by [ref] .

Applications of involutive Heegaard Floer homology · Splicing Seifert fibers · 0.80

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