scholarly journals Eta invariants and the hypoelliptic Laplacian

2019 ◽  
Vol 21 (8) ◽  
pp. 2355-2515 ◽  
Author(s):  
Jean-Michel Bismut
Keyword(s):  
Eta Invariants

scholarly journals Eta-invariants, torsion forms and flat vector bundles

2007 ◽  
Vol 340 (3) ◽  
pp. 569-624 ◽  
Author(s):  
Xiaonan Ma ◽  
Weiping Zhang
Keyword(s):  
Vector Bundles ◽  
Eta Invariants

scholarly journals Spectral Flow in Fredholm Modules, Eta Invariants and the JLO Cocycle

K-Theory ◽  
2004 ◽  
Vol 31 (2) ◽  
pp. 135-194 ◽  
Author(s):  
Alan Carey ◽  
John Phillips
Keyword(s):  
Spectral Flow ◽  
Eta Invariants

Eta-invariants and fermion number in finite volume

1992 ◽  
Vol 284 (3-4) ◽  
pp. 317-324
Author(s):  
Richard J. Szabo ◽  
Gordon W. Semenoff
Keyword(s):  
Finite Volume ◽  
Fermion Number ◽  
Eta Invariants

scholarly journals Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras

2019 ◽  
Author(s):  
Zhizhang Xie ◽  
Guoliang Yu
Keyword(s):  
Conjugacy Class ◽  
Discrete Group ◽  
Polynomial Growth ◽  
Algebraic Numbers ◽  
Eta Invariant ◽  
Trace Map ◽  
Novikov Conjecture ◽  
C Algebras ◽  
Eta Invariants ◽  
K Theory

Abstract In this paper, we establish a precise connection between higher rho invariants and delocalized eta invariants. Given an element in a discrete group, if its conjugacy class has polynomial growth, then there is a natural trace map on the $K_0$-group of its group $C^\ast$-algebra. For each such trace map, we construct a determinant map on secondary higher invariants. We show that, under the evaluation of this determinant map, the image of a higher rho invariant is precisely the corresponding delocalized eta invariant of Lott. As a consequence, we show that if the Baum–Connes conjecture holds for a group, then Lott’s delocalized eta invariants take values in algebraic numbers. We also generalize Lott’s delocalized eta invariant to the case where the corresponding conjugacy class does not have polynomial growth, provided that the strong Novikov conjecture holds for the group.

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