TY - JOUR

T1 - Non-abelian local invariant cycles

AU - Tsai, Yen Lung

AU - Xia, Eugene Z.

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2007/8

Y1 - 2007/8

N2 - Let f be a degeneration of Kähler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any coho-mology 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.

AB - Let f be a degeneration of Kähler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any coho-mology 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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U2 - 10.1090/S0002-9939-07-08843-0

DO - 10.1090/S0002-9939-07-08843-0

M3 - Article

AN - SCOPUS:77950639800

VL - 135

SP - 2365

EP - 2367

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -