Orthogonal group sections via light bulb systems

Yi Liu

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arXiv · 2610.27126

Orthogonal group sections via light bulb systems

Yi Liu

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Abstract

For any oriented, smooth $4$--manifold $X$ diffeomorphic to $(S^2\times S^2)^{\# n}\# D^4$, this paper shows that the natural group homomorphism $$\mathrm{Mod}(X,\partial X)\to \mathrm{O}(H_2(X;\mathbb{Z}))$$ admits a section. In fact, every light bulb system in $X$ gives rise to a section, which can be characterized uniquely in terms of implanted barbell twists and implanted crossbell involutions. Moreover, all sections arising from different light bulb systems become identical after a single $S^2\times S^2$--stabilization of $X$.

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Yi Liu. 2026-10-19. Orthogonal group sections via light bulb systems. https://arxiv.org/abs/2610.27126

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