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arXiv · 2606.27953

An Abstract Perturbation Theorem for Compact Moduli Spaces

Peter Albers·Irene Seifert·Tom Stalljohann
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Abstract

Given a compact zero set of a Fredholm section, our theorem guarantees the existence of a perturbed compact smooth manifold nearby, leaving the original zero set unaltered wherever transversality is already achieved. Such abstract perturbations allow for typical cobordism arguments. We illustrate this by re-proving a well-known theorem of Schwarz asserting the existence of critical points of the Hamiltonian action functional of different action values on symplectically aspherical manifolds.

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Peter Albers, Irene Seifert, Tom Stalljohann. 2026-06-26. An Abstract Perturbation Theorem for Compact Moduli Spaces. https://arxiv.org/abs/2606.27953

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