On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes

Yoshiyasu Fukumoto

RECORD

On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes

Yoshiyasu Fukumoto

K-Theory and Homology · Submitted 2 Apr 2016

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

The authors' main claim The main result of this paper is non-vanishing of the image of the index map from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$ to the $K$-theory of the $C^{*}$-algebra of the group $G$.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1604.00464 (version 2)

Pith IDNZLSR4EI, Pith's permanent record of this paper and its review

CitationYoshiyasu Fukumoto. "On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes." arXiv:1604.00464 (2016). https://pith.science/paper/NZLSR4EI

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,761 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The main result of this paper is non-vanishing of the image of the index map from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$ to the $K$-theory of the $C^{*}$-algebra of the group $G$. Under the assumption that the Kronecker pairing of a $K$-homology class with a low-dimensional cohomology class is non-zero, we prove that the image of this class under the index map is non-zero. Neither discreteness of the locally compact group $G$ nor freeness of the action of $G$ on $X$ are required. The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.

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	The main result of this paper is non-vanishing of the image of the index map from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$ to the $K$-theory of the $C^{*}$-algebra of the group $G$.	result 0.97	0.94	0.98	asserted 1.00
s1	Under the assumption that the Kronecker pairing of a $K$-homology class with a low-dimensional cohomology class is non-zero, we prove that the image of this class under the index map is non-zero.	result 0.86	0.94	0.24	asserted 1.00
s2	Neither discreteness of the locally compact group $G$ nor freeness of the action of $G$ on $X$ are required.	contribution 0.61	0.65	0.04	asserted 1.00
s3	The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.	background 0.99	0.03	0.01	asserted 1.00

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

What was examined, and what was not

sources read

arXiv listing abstract v2

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

The main result of this paper is non-vanishing of the image of the index map from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$ to the $K$-theory of the $C^{*}$-algebra of the group $G$. Under the assumption that the Kronecker pairing of a $K$-homology class with a low-dimensional cohomology class is non-zero, we prove that the image of this class under the index map is non-zero. Neither discreteness of the locally compact group $G$ nor freeness of the action of $G$ on $X$ are required. The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.

Human review

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

How the literature uses it

2 arXiv papers cite this in 7 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 · 5 sentences without a confident label

Builds on it 1 paper

Although the $G$-manifold should be connected in [ref] , however in this case, we can apply it to $Z$ after replacing some arguments in [ref] as follows.

$G$-Homotopy Invariance of the Analytic Signature of Proper Co-compact $G$-manifolds and Equivariant Novikov Conjecture · On proof of Corollary [ref] · 0.96

Uses its method or tool 1 paper

[ref] When constructing a $U(1)$-valued cocycle $α∈Z(G;U(1))$ from the given line bundle, we just use a line bundle $L$ over $X$ ignoring $f_^*$ over $Y$.

$G$-Homotopy Invariance of the Analytic Signature of Proper Co-compact $G$-manifolds and Equivariant Novikov Conjecture · On proof of Corollary [ref] · 0.84

Discussion

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