scholarly journals Algebraic K-theory of group rings and the cyclotomic trace map

2017 ◽  
Vol 304 ◽  
pp. 930-1020 ◽  
Author(s):  
Wolfgang Lück ◽  
Holger Reich ◽  
John Rognes ◽  
Marco Varisco
Keyword(s):  
Group Rings ◽  
Trace Map ◽  
K Theory

scholarly journals Higher K -theory of group-rings of virtually infinite cyclic groups

2003 ◽  
Vol 325 (4) ◽  
pp. 711-726 ◽  
Author(s):  
Aderemi O. Kuku ◽  
Guoping Tang
Keyword(s):  
Group Rings ◽  
Cyclic Groups ◽  
K Theory

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 Calculation of Two-Primary Algebraic K -Theory of Some Group Rings

K-Theory ◽  
1999 ◽  
Vol 16 (4) ◽  
pp. 391-397 ◽  
Author(s):  
Paul arne østvær
Keyword(s):  
Group Rings ◽  
K Theory

K -Theory for Twisted Group Rings

1974 ◽  
Vol s3-29 (2) ◽  
pp. 257-271 ◽  
Author(s):  
S. M. J. Wilson
Keyword(s):  
Group Rings ◽  
Twisted Group ◽  
K Theory
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