Rozansky-Witten invariants via formal geometry

M. Kontsevich

RECORD

Rozansky-Witten invariants via formal geometry

M. Kontsevich

dg-ga · Submitted 19 Apr 1997

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

The authors' main claim We show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from Gelfand-Fuks cohomology.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,993 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.65 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from Gelfand-Fuks cohomology. In particular, any symplectic foliation gives invariants of 3-manifolds. Our preprint has many intersections with the preprint alg-geom/9704009 by M.Kapranov.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from Gelfand-Fuks cohomology.	result 0.63	0.88	0.89	asserted 1.00
s1	In particular, any symplectic foliation gives invariants of 3-manifolds.	result 0.74	0.63	0.17	asserted 1.00
s2	Our preprint has many intersections with the preprint alg-geom/9704009 by M.Kapranov.	background 0.84	0.24	0.03	asserted 0.96

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.93.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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 show that recently constructed invariants of 3-dimensional manifolds and of hyperkaehler manifolds (L.Rozansky and E.Witten, hep-th/9612216) come from characteristic classes of foliations and from Gelfand-Fuks cohomology. In particular, any symplectic foliation gives invariants of 3-manifolds. Our preprint has many intersections with the preprint alg-geom/9704009 by M.Kapranov.

Human review

How Pith checks papers → · Full audit of this paper →

References

How the literature uses it

6 arXiv papers cite this in 10 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 · 8 sentences without a confident label

Cites it as background 2 papers

Rozansky–Witten models are topological twists of 3-dimensional $𝒩=4$ supersymmetric sigma models with holomorphic symplectic target manifolds [ref] .

Truncated affine Rozansky--Witten models as extended defect TQFTs · Introduction and summary · 1.00
This structure plays an important role in the construction of Rozansky–Witten invariants [ref] , which are parity-shifted analogues of the Chern–Simons invariants of three-manifolds.

Atiyah classes and dg-Lie algebroids for matched pairs · Introduction · 0.92

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.