Instanton Floer homology for lens spaces

Abstract

We construct instanton Floer homology for lens spaces $L(p,q)$. As an application, we prove that $X = \CP^2 # \CP^2$ does not admit a decomposition $X=X_1\cup X_2$. Here $X_1$ and $X_2$ are oriented, simply connected, non-spin 4-manifolds with $b^{+}=1$ and with boundary $L(p,2)$, and $p$ is a prime number of the form $16N+1$.

33 pages: an error in Section 4.2 is corrected: Section 4.3 and 4.4 are rewritten

References in corpus (2)

• An SO(3)-version of 2-torsion instanton invariants
• Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting