scholarly journals Equivariant Novikov conjecture for groups acting on Euclidean buildings

1998 ◽  
Vol 350 (6) ◽  
pp. 2141-2183 ◽  
Author(s):  
Donggeng Gong
Keyword(s):  
Novikov Conjecture ◽  
Euclidean Buildings

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

Non-discrete Euclidean buildings for the Ree and Suzuki groups

2010 ◽  
Vol 132 (4) ◽  
pp. 1113-1152 ◽  
Author(s):  
Petra Hitzelberger ◽  
Linus Kramer ◽  
Richard M. Weiss
Keyword(s):  
Suzuki Groups ◽  
Euclidean Buildings

scholarly journals A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings

2018 ◽  
Vol 22 (7) ◽  
pp. 3827-3923 ◽  
Author(s):  
Michael Kapovich ◽  
Bernhard Leeb ◽  
Joan Porti
Keyword(s):  
Symmetric Spaces ◽  
Euclidean Buildings

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.

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