Donaldson invariants for connected sums along surfaces of genus 2

DOI10.1016/S0166-8641(99)00107-8zbMATH Open0957.57023arXivdg-ga/9702004OpenAlexW2171468963MaRDI QIDQ1585736

Vicente Muñoz

Publication date: 22 March 2001

Published in: Topology and its Applications (Search for Journal in Brave)

Abstract: We relate the Donaldson invariants of two four-manifolds $X_i$ with embedded Riemann surfaces of genus 2 and self-intersection zero with the invariants of the manifold X which appears as a connected sum along the surfaces. When the original manifolds are of simple type with $b_1=0$ and $b^{+}>1$, X is of simple type with $b_1=0$ and $b^{+}>1$ as well, and the relationship between the invariants is expressed as constraints in the basic classes for X. Also we give some applications. For instance, if $X_i$ have both $b_1=0$ then X is of simple type with $b_1=0$, $b^{+}>1$, and has no basic classes evaluating zero on the Riemann surface. Finally, we prove that any four-manifold with $b^{+}>1$ and with an embedded surface of genus 2, self-intersection zero and representing an odd homology class, is of finite type of second order.

Full work available at URL: https://arxiv.org/abs/dg-ga/9702004

zbMATH Keywords

4-manifoldsFukaya-Floer (co)homology

Mathematics Subject Classification ID

Applications of global analysis to structures on manifolds (57R57)

Related Items (2)

Four-manifold invariants from higher-rank bundles ⋮ SU(2)-Donaldson invariants of the complex projective plane

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