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Sur la topologie de l'espace des operateurs pseudodifferentiels inversibles d'ordre 0

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Frederic Rochon

Differential Geometry · Submitted 19 Oct 2006

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

The authors' main claim The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X.

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arXiv IDmath/0610576 (version 3)
Pith ID4RDMNJSE, Pith's permanent record of this paper and its review
CitationFrederic Rochon. "Sur la topologie de l'espace des operateurs pseudodifferentiels inversibles d'ordre 0." arXiv:math/0610576 (2006). https://pith.science/paper/4RDMNJSE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,581 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.08 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; .

The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. At the same time, we show that the subgroup of invertible compact perturbations of the identity is weakly retractable inside this group. These results are also adapted to the case of suspended operators. Some applications in index theory and for the residue determinant of Simon Scott are also given.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. result 0.95 0.92 0.85 asserted 1.00
s1 At the same time, we show that the subgroup of invertible compact perturbations of the identity is weakly retractable inside this group. result 0.99 0.95 0.11 asserted 1.00
s2 These results are also adapted to the case of suspended operators. result 0.55 0.89 0.05 asserted 0.99
s3 Some applications in index theory and for the residue determinant of Simon Scott are also given. contribution 0.67 0.81 0.05 asserted 0.97

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

The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. At the same time, we show that the subgroup of invertible compact perturbations of the identity is weakly retractable inside this group. These results are also adapted to the case of suspended operators. Some applications in index theory and for the residue determinant of Simon Scott are also given.

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