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Non-abelian Local Invariant Cycles

Yen-lung Tsai·Eugene Z. Xia
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Abstract

Let f be a degeneration of Kahler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any cohomology class, invariant under the monodromy action, rises 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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Yen-lung Tsai, Eugene Z. Xia. 2004-11-23. Non-abelian Local Invariant Cycles. https://arxiv.org/abs/math/0411504

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