The Atiyah conjecture

2016 ◽  
pp. 198-220
Author(s):  
Peter A. Linnell
Keyword(s):  
Atiyah Conjecture

scholarly journals The strong Atiyah conjecture for right-angled Artin and Coxeter groups

2011 ◽  
Vol 158 (1) ◽  
pp. 261-266 ◽  
Author(s):  
Peter Linnell ◽  
Boris Okun ◽  
Thomas Schick
Keyword(s):  
Coxeter Groups ◽  
Atiyah Conjecture

scholarly journals On computing homology gradients over finite fields

2016 ◽  
Vol 162 (3) ◽  
pp. 507-532 ◽  
Author(s):  
ŁUKASZ GRABOWSKI ◽  
THOMAS SCHICK
Keyword(s):  
Finite Fields ◽  
Group Ring ◽  
Spectral Measure ◽  
Irrational Number ◽  
Betti Numbers ◽  
Universal Cover ◽  
Specific Method ◽  
Arbitrary Characteristic ◽  
Cw Complex ◽  
Atiyah Conjecture

AbstractRecently the so-called Atiyah conjecture about l2-Betti numbers has been disproved. The counterexamples were found using a specific method of computing the spectral measure of a matrix over a complex group ring. We show that in many situations the same method allows to compute homology gradients, i.e. generalisations of l2-Betti numbers to fields of arbitrary characteristic. As an application we point out that (i) the homology gradient over any field of characteristic different than 2 can be an irrational number, and (ii) there exists a finite CW-complex with the property that the homology gradients of its universal cover taken over different fields have infinitely many different values.

scholarly journals The Atiyah conjecture for the Hecke algebra of the infinite dihedral group

2014 ◽  
Vol 8 (4) ◽  
pp. 1161-1194 ◽  
Author(s):  
Boris Okun ◽  
Richard Scott
Keyword(s):  
Dihedral Group ◽  
Hecke Algebra ◽  
Atiyah Conjecture

scholarly journals ApproximatingL2-invariants and the Atiyah conjecture

2003 ◽  
Vol 56 (7) ◽  
pp. 839-873 ◽  
Author(s):  
J�zef Dodziuk ◽  
Peter Linnell ◽  
Varghese Mathai ◽  
Thomas Schick ◽  
Stuart Yates
Keyword(s):  
Atiyah Conjecture

The Atiyah Conjecture and $$L^2$$ L 2 -cohomology computations

2017 ◽  
Vol 195 (1) ◽  
pp. 339-364
Author(s):  
Wiktor Mogilski ◽  
Kevin Schreve
Keyword(s):  
Atiyah Conjecture

scholarly journals The Atiyah Conjecture and Artinian Rings

2012 ◽  
Vol 8 (2) ◽  
pp. 313-328 ◽  
Author(s):  
Peter A. Linnell ◽  
Thomas Schick
Keyword(s):  
Artinian Rings ◽  
Atiyah Conjecture

scholarly journals Finite group extensions and the Atiyah conjecture

2007 ◽  
Vol 20 (04) ◽  
pp. 1003-1052 ◽  
Author(s):  
Peter Linnell ◽  
Thomas Schick
Keyword(s):  
Finite Group ◽  
Group Extensions ◽  
Atiyah Conjecture
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