Real embedding and equivariant eta forms

Bo Liu

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Real embedding and equivariant eta forms

Bo Liu

Differential Geometry · Submitted 21 Jun 2017

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

The authors' main claim In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case.

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

In 1993, Bismut and Zhang establish a mod Z embedding formula of Atiyah-Patodi-Singer reduced eta invariants. In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case. In this case, the spectral flow is generalized to the equivariant chern character of some equivariant Dai-Zhang higher spectral flow.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In 1993, Bismut and Zhang establish a mod Z embedding formula of Atiyah-Patodi-Singer reduced eta invariants.	background 1.00	0.03	0.04	asserted 1.00
s1	In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case.	contribution 1.00	0.93	0.68	asserted 1.00
s2	In this case, the spectral flow is generalized to the equivariant chern character of some equivariant Dai-Zhang higher spectral flow.	contribution 0.69	0.71	0.21	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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The paper

Original abstract

In 1993, Bismut and Zhang establish a mod Z embedding formula of Atiyah-Patodi-Singer reduced eta invariants. In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case. In this case, the spectral flow is generalized to the equivariant chern character of some equivariant Dai-Zhang higher spectral flow.

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1 arXiv paper cite this in 1 sentence

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

What it cites · 13 sentences without a confident label

Builds on 1 paper

The following theorem is the Clifford module version of [ref] , which is related to [ref] , [ref] and [ref] .

Equivariant eta forms and equivariant differential $K$-theory · Functoriality · 0.93

Uses the method or tool of 1 paper

Thanks to the functoriality of equivariant eta forms proved in [ref] , we only need to prove the embedding formula when $B$ is a point and $X$ is odd.

Equivariant eta forms and equivariant differential $K$-theory · Introduction · 0.82

Compares with 1 paper

Our main result here is expected to play the same role in the equivariant differential K-theory of the Bunke-Schick model [ref] as the Bismut-Lebeau embedding formula [ref] does in the proof of Arithmetic Grothendieck-Riemann-Roch theorem in Arakelov geometry.

Equivariant eta forms and equivariant differential $K$-theory · Introduction · 0.82

Cites as background 1 paper

In Section 1, we summarize the definition and the properties of equivariant eta forms in [ref] using the language of Clifford modules.

Equivariant eta forms and equivariant differential $K$-theory · Introduction · 0.81

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