On finite symmetries of simply connected four-manifolds

zbMATH Open1377.57029arXiv1607.02776MaRDI QIDQ323944

Ioana Şuvaina

Publication date: 10 October 2016

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Abstract: For most positive integer pairs $(a,b)$, the topological space $$ is shown to admit infinitely many inequivalent smooth structures which dissolve upon performing a single connected sum with $S^{2}imes{S}^2$. This is then used to construct infinitely many non-equivalent smooth free actions of suitable finite groups on the connected sum $$. We then investigate the behavior of the sign of the Yamabe invariant for the resulting finite covers, and observe that these constructions provide many new counter-examples to the $4$-dimensional Rosenberg Conjecture.

Full work available at URL: https://arxiv.org/abs/1607.02776

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zbMATH Keywords

4-manifoldsSeiberg-Witten invariantsYamabe invariantBauer-Furuta invariantsRosenberg conjecture

Mathematics Subject Classification ID

Applications of global analysis to structures on manifolds (57R57) Differentiable structures in differential topology (57R55) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (8)

On the topology of nonnegatively curved simply connected 4-manifolds with continuous symmetry ⋮ Nonlocally smoothable topological symmetries of four-manifolds ⋮ A proof of a theorem of Luttinger and Simpson about the number of vanishing circles of a near-symplectic form on a 4-dimensional manifold ⋮ Characteristic cohomotopy classes for families of 4-manifolds ⋮ 4-fold symmetric quandle invariants of 3-manifolds ⋮ Minimizing Euler characteristics of symplectic four-manifolds ⋮ Minimality and irreducibility of symplectic four-manifolds ⋮ Symmetry groups of four-manifolds

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