scholarly journals Maximal rigid subalgebras of deformations and L2-cohomology

2021 ◽  
Vol 14 (7) ◽  
pp. 2269-2306
Author(s):  
Rolando de Santiago ◽  
Ben Hayes ◽  
Daniel J. Hoff ◽  
Thomas Sinclair
Keyword(s):  
L2 Cohomology

scholarly journals L2 -cohomology of manifolds with flat ends

2003 ◽  
Vol 13 (2) ◽  
pp. 366-395 ◽  
Author(s):  
C. Carron
Keyword(s):  
L2 Cohomology

Some New Results on L2 Cohomology of Negatively Curved Riemannian Manifolds

2005 ◽  
Vol 57 (2) ◽  
pp. 251-266
Author(s):  
M. Cocos
Keyword(s):  
Heat Equation ◽  
Riemannian Manifolds ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Regularity Properties ◽  
L2 Cohomology ◽  
Cohomology Spaces

AbstractThe present paper is concerned with the study of the L2 cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial L2 cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.

Von Neumann Categories and Extended L2 Cohomology

K-Theory ◽  
1998 ◽  
Vol 15 (4) ◽  
pp. 347-405 ◽  
Author(s):  
Michael Farber
Keyword(s):  
Von Neumann ◽  
L2 Cohomology

scholarly journals L2-Cohomology and group cohomology

Topology ◽  
1986 ◽  
Vol 25 (2) ◽  
pp. 189-215 ◽  
Author(s):  
Jeff Cheeger ◽  
Mikhael Gromov
Keyword(s):  
Group Cohomology ◽  
L2 Cohomology

scholarly journals L2 TORSION WITHOUT THE DETERMINANT CLASS CONDITION AND EXTENDED L2 COHOMOLOGY

2005 ◽  
Vol 07 (04) ◽  
pp. 421-462 ◽  
Author(s):  
MAXIM BRAVERMAN ◽  
ALAN CAREY ◽  
MICHAEL FARBER ◽  
VARGHESE MATHAI
Keyword(s):  
Type Theorem ◽  
Abelian Category ◽  
Von Neumann ◽  
L2 Cohomology ◽  
Recent Theorem ◽  
Additional Assumptions

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L2 cohomology. Under the determinant class assumption the L2 torsions of this paper specialize to the invariants studied in our previous work [6]. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler [3] we obtain a Cheeger–Müller type theorem stating the equality between the combinatorial and the analytic L2 torsions.

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