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Non-abelian local invariant cycles

Authors: Yen-lung Tsai and Eugene Z. Xia
Journal: Proc. Amer. Math. Soc. 135 (2007), 2365-2367
MSC (2000): Primary 14D05, 20F34, 55N20
Published electronically: March 22, 2007
MathSciNet review: 2302557
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Abstract: Let $f$ 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

Eugene Z. Xia
Affiliation: Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan

Received by editor(s): December 6, 2004
Received by editor(s) in revised form: April 18, 2006
Published electronically: 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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.