scholarly journals The Equivariant Coarse Novikov Conjecture and Coarse Embedding

2020 ◽  
Vol 380 (1) ◽  
pp. 245-272
Author(s):  
Benyin Fu ◽  
Xianjin Wang ◽  
Guoliang Yu
Keyword(s):  
Novikov Conjecture ◽  
Coarse Embedding

scholarly journals A comment on the Novikov conjecture

1981 ◽  
Vol 83 (3) ◽  
pp. 656-656 ◽  
Author(s):  
Jerome Kaminker ◽  
John G. Miller
Keyword(s):  
Novikov Conjecture

scholarly journals The Novikov conjecture

2019 ◽  
Vol 74 (3) ◽  
pp. 525-541
Author(s):  
G. Yu
Keyword(s):  
Novikov Conjecture

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.

scholarly journals The Novikov conjecture and geometry of Banach spaces

2012 ◽  
Vol 16 (3) ◽  
pp. 1859-1880 ◽  
Author(s):  
Gennadi Kasparov ◽  
Guoliang Yu
Keyword(s):  
Banach Spaces ◽  
Novikov Conjecture
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