×

Signature of 4-manifolds with circle action. (Chinese. English summary) Zbl 1265.57012

Summary: It is proved that for a 4-dimensional connected closed \(S^1\)-manifold \(M\) with non-empty finite fixed point set, the equivariant cohomology ring \(H^*_G (M; \mathbb Q)\) of \(M\) with coefficients in \(\mathbb Q\), is a free \(H^* (BG; \mathbb Q)\) module. The main result is about the relationship between the signature \(\sigma (M)\) of \(M\) and the number of the fixed points \(|M^G|\).

MSC:

57R91 Equivariant algebraic topology of manifolds
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
57S10 Compact groups of homeomorphisms
PDFBibTeX XMLCite