arXiv:2611.13119v1 Announce Type: new Abstract: We study closed Reeb orbits on prequantization circle bundles $(M,\xi)\to(B,\omega)$ with $c_1(\xi)|_{\pi_2(M)}=0$. When $\omega|_{\pi_2(B)}\ne0$, we construct augmentations and compute contractible linearized contact homology as a direct sum of shifted copies of $H_*(B;\mathbb Q)$, under a condition on the rational Betti numbers of $B$. The construction uses Morse-Bott methods and requires neither a filling nor index-admissibility. When $c_1(TB)|_{\pi_2(B)}\ne0$, index recurrence and Morse inequalities yield multiplicity and non-hyperbolicity bounds for nondegenerate contact forms under additional index assumptions. If $c_1(TB)|_{\pi_2(B)}=0$ and either $H_{\mathrm{odd}}(B;\mathbb Q)=0$ or $\omega|_{\pi_2(B)}=0$, every nondegenerate supporting contact form has infinitely many simple closed Reeb orbits. We also establish multiplicity and non-hyperbolicity results for smooth prequantizations of symplectic orbifolds admitting Hamiltonian circle actions with isolated fixed points.
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