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RESEARCH BLOG 4/1/03 Walter Neumann discussed the Casson invariant conjecture at the
 

Summary: RESEARCH BLOG 4/1/03
Walter Neumann discussed the Casson invariant conjecture at the
Spring Topology and Dynamical Systems Conference. This conjecture
states that for a homology sphere 3
which is the link of a complete
intersection complex surface singularity, the Casson invariant () is
1
8
the signature of the Milnor fiber. I'm not going to describe this con-
jecture, but apparently Neumann and his collaborator Jonathan Wahl
have made some progress on this (see the papers at Neumann's web
page) by computing both the Casson invariant and the signature of
the Milnor fiber for a special class of examples. Chris Herald gave a
talk generalizing the Casson invariant, using a count of flat SU(3) con-
nections, and his attempt to generalize this to SU(n). I don't really
understand this stuff too well, but it would be nice to have a more
topological way of defining the Casson and related invariants. Hyam
Rubinstein and Weiping Li showed that the Casson invariant is a ho-
motopy invariant.
One possible way one might be able to get the Casson invariant in a

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics