The DOI matches its Crossref record; 12 of the 13 references it cites were found in a registry or an index; none of the 13 sources its claims cite is checked for support yet.
The adams conjecture
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Claims the paper makes
0 Valid · 2 Not valid · 13 Not checked · 30 Own results and interpretations
In the paper
“LEMMA 4.6.The mod 2 cohor~~ology of n dihedral group is detected bj* its family of elementary abelian 2-subgroups.”
§ Prm~ed in Great Brirain THE ADAMS CONJECTURE > Choosing an invariant complementary
What the sources say
- Not matchedcites [I 21
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
A result the paper states — it cites no source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“PROPOSITION 1.2.The Adams conjecture is true for any cirtual bundle whose structural group may be reduced to a finite group.”
§ Prm~ed in Great Brirain THE ADAMS CONJECTURE > Sl. PLAN OF THE DEMONSTRATION
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We show in the appendix to this paper (5.5) that ifp is odd and if G leaves invariant a non-degenerate symmetric bilinear form on c', then x is the character of an element of the real representation ring RO(G).”
§ Prm~ed in Great Brirain THE ADAMS CONJECTURE > Sl. PLAN OF THE DEMONSTRATION
boostedstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Rests on an assumption not shown here.
None of the sources cited for this claim have been checked yet.
In the paper
“LEMMA 2.4. Every element of RO(G) is an integral linear combination of representations inducedfrom one and two dimensional representations of subgroups of G.”
§ Prm~ed in Great Brirain THE ADAMS CONJECTURE > LEMMA 2.4. Every element of RO(G) is an integral linear combination of representations inducedfrom one and two dimensional representations of subgroups of G.
What the sources say
- Not matchedcites [14, pp. 1 I-291]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked — no full text of the sourcecites [6] Borel, 1953, Sur certains sous-groupes des groupes de Lie compacts, Comment. Math. Helvet. source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
A result the paper states — it cites no source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If y E KO( Y) then f* Ypy = 'rpf* y in KO(X)[p-'1.”
§ Prm~ed in Great Brirain THE ADAMS CONJECTURE > RSp,(G)).
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
26 more claims
Create a free account to see all 45 claims and every source verdict.
- It may state two separate claims as one. 13
- The quote only partly states this claim. 1
- Probably not a substantial claim. 1
Citations
Cites
Adams, J. F. (1966) · Topology · doi:10.1016/0040-9383(66)90004-8 · Cited by 589
The characters of the finite general linear groups
Green, J. A. (1955) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1955-0072878-2 · Cited by 489
The index of elliptic operators, II
Atiyah, M. F., & Segal, G. B. (1968) · The Annals of Mathematics · doi:10.2307/1970716 · Cited by 461
Chevalley, C. (1955) · Tohoku Mathematical Journal · doi:10.2748/tmj/1178245104 · Cited by 435
Group representations, λ-rings and the J-homomorphism
Atiyah, M. F., & Tall, D. O. (1969) · Topology · doi:10.1016/0040-9383(69)90015-9 · Cited by 194
Atiyah, M. F. (1961) · Proceedings of the London Mathematical Society · doi:10.1112/plms/s3-11.1.291 · Cited by 186
Homology of the infinite symmetric group
Nakaoka, M. (1961) · The Annals of Mathematics · doi:10.2307/1970333 · Cited by 109
Adams, J. F. (1963) · Topology · doi:10.1016/0040-9383(63)90001-6 · Cited by 90
Sur certains sous-groupes des groupes de Lie compacts
Borel, A., & Serre, J. P. (1953) · Commentarii Mathematici Helvetici · doi:10.1007/bf02564557 · Cited by 87
The K-theory of Eilenberg-Maclane complexes
Anderson, D. W., & Hodgkin, L. (1968) · Topology · doi:10.1016/0040-9383(68)90009-8 · Cited by 82
Research works printed but not linked: 1
- Sullivan, 1970, Lectures given at The Institute for Advanced Study
Cited by
On the Cohomology and K-Theory of the General Linear Groups Over a Finite Field
Quillen, D. G. (1972) · Annals of Mathematics · doi:10.2307/1970825 · Cited by 487
Self-citationGenetics of Homotopy Theory and the Adams Conjecture
Sullivan, D. (1974) · The Annals of Mathematics · doi:10.2307/1970841 · Cited by 276
The transfer map and fiber bundles
Becker, J. C., & Gottlieb, D. H. (1975) · Topology · doi:10.1016/0040-9383(75)90029-4 · Cited by 195
“1 (Quillen [21], Sullivan [25], Friedlander [1 11).”
BackgroundMethodApplications of the transfer to stable homotopy theory
Kahn, D. S., & Priddy, S. B. (1972) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1972-13076-3 · Cited by 151
On a space between $BH$ and $B_\infty$
Madsen, I. (1975) · Pacific Journal of Mathematics · doi:10.2140/pjm.1975.60.235 · Cited by 123
Metadata
- Authors
- Quillen, D.
- Corresponding author
- Quillen, Daniel
- Venue
- Topology
- Publisher
- Elsevier BV
- Published
- 1971-03
- Volume
- 10
- Issue
- 1
- Pages
- 67-80
- ISSN
- 0040-9383 (ISSN-L)
- OpenAlex
- W2092511048
- Semantic Scholar
- 3393af5cd8dc60da283a5cf96546fe45b8ed80ca
- Cited by
- 195
- References
- 13
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 5 · 2023: 3 · 2022: 1 · 2021: 6 · 2020: 3 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 11 · 2015: 2 · 2014: 2 · 2013: 4 · 2012: 2
- FWCI
- 8.26
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (vor, 15480 d)
- Locations
- Topology (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Algebra and Number Theory › Advanced Algebra and Geometry
- Keywords
- real vector bundles, modular representations, algebraic topology
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
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How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The adams conjecture. https://app.cochat.ai/papers/10.1016/0040-9383(71)90018-8
- The paper
- Quillen, D. (1971). The adams conjecture. Topology. https://doi.org/10.1016/0040-9383(71)90018-8
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
