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A note on invertibility of the Dirac operator twisted with Hilbert-A-module coefficients

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Thomas Schick (Universität Göttingen)

Differential Geometry · Submitted 10 Jan 2021

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

The authors' main claim Given a closed connected spin manifold M with non-negative and somewhere positive scalar curvature, we show that the Dirac operator twisted with any flat Hilbert module bundle is invertible.

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arXiv ID2101.03595 (version 2)
Pith IDEZXVTFDI, Pith's permanent record of this paper and its review
CitationThomas Schick (Universit\"at G\"ottingen). "A note on invertibility of the Dirac operator twisted with Hilbert-A-module coefficients." arXiv:2101.03595 (2021). https://pith.science/paper/EZXVTFDI
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,624 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.01.

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

Given a closed connected spin manifold M with non-negative and somewhere positive scalar curvature, we show that the Dirac operator twisted with any flat Hilbert module bundle is invertible.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Given a closed connected spin manifold M with non-negative and somewhere positive scalar curvature, we show that the Dirac operator twisted with any flat Hilbert module bundle is invertible. result 0.96 0.94 0.95 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

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Original abstract

Given a closed connected spin manifold M with non-negative and somewhere positive scalar curvature, we show that the Dirac operator twisted with any flat Hilbert module bundle is invertible.

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