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Topology of Stratified Spaces MSRI Publications
 

Summary: Topology of Stratified Spaces
MSRI Publications
Volume 58, 2010
An introduction to L2
cohomology
XIANZHE DAI
ABSTRACT. After a quick introduction to L2
cohomology, we discuss recent
joint work with Jeff Cheeger where we study, from a mostly topological stand-
point, the L2
-signature of certain spaces with nonisolated conical singularities.
The contribution from the singularities is identified with a topological invariant
of the link fibration of the singularities, involving the spectral sequence of the
link fibration.
This paper consists of two parts. In the first, we give an introduction to
L2 cohomology. This is partly based on [8]. We focus on the analytic aspect
of L2 cohomology theory. For the topological story, we refer to [1; 22; 31]
and of course the original papers [16; 17]. For the history and comprehensive
literature, see [29]. The second part is based on our joint work with Jeff Cheeger
[11], which gives the contribution to the L2 signature from nonisolated conical

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics