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  "body": "\n## Summary\n\nThe Casson invariant is an integer-valued invariant of oriented integral [[homology 3-spheres|HK8NS02NNE]], introduced by Andrew Casson.\nInformally it counts, with signs, the irreducible representations of the fundamental group into $SU(2)$, up to conjugation, divided by $2$.\nIt reduces modulo $2$ to the Rokhlin invariant, and it has a simple behaviour under [[Dehn surgery|ZA405B0Z1S]] on knots.\nIt was one of the first gauge-theoretic style invariants of $3$-manifolds and led to instanton Floer homology.\n\n## Explanations\n\n### L1 human\n\nA homology $3$-sphere looks like the $3$-sphere to homology, but may be very different.\nThe Casson invariant is a whole number attached to each one, and it is $0$ for the $3$-sphere.\nWhen it is not $0$, the fundamental group has a nontrivial representation into the group of unit quaternions, so the manifold cannot be the $3$-sphere.\nFor the Poincaré homology sphere it equals $\\pm 1$, depending on the orientation.\n",
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