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The $\bar\mu$-invariant of Seifert fibered homology spheres and the Dirac operator

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Daniel Ruberman, Nikolai Saveliev

Geometric Topology · Submitted 16 Sep 2010

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

The authors' main claim We derive a formula for the $\bar\mu$-invariant of a Seifert fibered homology sphere in terms of the eta-invariant of its Dirac operator.

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arXiv ID1009.3201 (version 1)
Pith IDJFVLSWDO, Pith's permanent record of this paper and its review
CitationDaniel Ruberman, Nikolai Saveliev. "The $\bar\mu$-invariant of Seifert fibered homology spheres and the Dirac operator." arXiv:1009.3201 (2010). https://pith.science/paper/JFVLSWDO
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,314 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We derive a formula for the $\bar\mu$-invariant of a Seifert fibered homology sphere in terms of the eta-invariant of its Dirac operator. As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We derive a formula for the $\bar\mu$-invariant of a Seifert fibered homology sphere in terms of the eta-invariant of its Dirac operator. result 0.79 0.95 0.82 asserted 1.00
s1 As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres. result 0.86 0.93 0.25 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 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 derive a formula for the $\bar\mu$-invariant of a Seifert fibered homology sphere in terms of the eta-invariant of its Dirac operator. As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres.

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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

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