On Casson-type instanton moduli spaces over negative definite four-manifolds - Mathematics > Geometric TopologyReportar como inadecuado




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Abstract: Recently Andrei Teleman considered instanton moduli spaces over negativedefinite four-manifolds $X$ with $b 2X \geq 1$. If $b 2X$ is divisible byfour and $b 1X =1$ a gauge-theoretic invariant can be defined; it is a countof flat connections modulo the gauge group. Our first result shows that if sucha moduli space is non-empty and the manifold admits a connected sumdecomposition $X \cong X 1 # X 2$ then both $b 2X 1$ and $b 2X 2$ aredivisible by four; this rules out a previously natural appearing source of4-manifolds with non-empty moduli space. We give in some detail a constructionof negative definite 4-manifolds which we expect will eventually provideexamples of manifolds with non-empty moduli space.



Autor: Andrew Lobb, Raphael Zentner

Fuente: https://arxiv.org/







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