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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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: https://doi.org/10.1090/S0002-9939-07-08843-0
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.