The Topology of Compact Lie Group Actions through the Lens of Finite Models
نویسندگان
چکیده
Given a compact, connected Lie group K, we use principal K-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let M be a compact, connected, smooth manifold which supports an almost free K-action. Under a partial formality assumption on the orbit space and a regularity assumption on the characteristic classes of the action, we describe an algebraic model for M with commensurate finiteness and partial formality properties. The existence of such a model has various implications on the structure of the cohomology jump loci of M and of the representation varieties of π1pMq. As an application, we show that compact Sasakian manifolds of dimension 2n ` 1 are pn ́ 1q-formal, and that their fundamental groups are filtered-formal. Further applications to the study of weighted-homogeneous isolated surface singularities are also given.
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