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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Non-abelian local invariant cycles
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by Yen-lung Tsai and Eugene Z. Xia PDF
Proc. Amer. Math. Soc. 135 (2007), 2365-2367 Request permission

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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2365-2367
  • MSC (2000): Primary 14D05, 20F34, 55N20
  • DOI: https://doi.org/10.1090/S0002-9939-07-08843-0
  • MathSciNet review: 2302557