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Non-abelian local invariant cycles
Author(s):
Yen-lung
Tsai;
Eugene
Z.
Xia
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2365-2367.
MSC (2000):
Primary 14D05, 20F34, 55N20
Posted:
March 22, 2007
MathSciNet review:
2302557
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Additional information
Abstract:
Let  be a degeneration of Kähler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any cohomology class, invariant under the monodromy action, comes from a global cohomology class. Instead of the classical cohomology, one may consider the non-abelian cohomology. This note demonstrates that the analogous non-abelian version of the local invariant cycle theorem does not hold if the first non-abelian cohomology is the moduli space (universal categorical quotient) of the representations of the fundamental group.
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Additional Information:
Yen-lung
Tsai
Affiliation:
Department of Mathematical Sciences, National Chengchi University, Taipei 116, Taiwan
Email:
yenlung@math.nccu.edu.tw
Eugene
Z.
Xia
Affiliation:
Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan
Email:
ezxia@ncku.edu.tw
DOI:
10.1090/S0002-9939-07-08843-0
PII:
S 0002-9939(07)08843-0
Received by editor(s):
December 6, 2004
Received by editor(s) in revised form:
April 18, 2006
Posted:
March 22, 2007
Additional Notes:
Tsai is partially supported by the National Center for Theoretical Sciences, Hsinchu, Taiwan; Xia gratefully acknowledges partial support by National Science Council Taiwan grant NSC 93-2115-M-006-002.
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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