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arXiv · 2505.12876

What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers

Philipp Berghofer·Jordan François·Lucrezia Ravera
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Abstract

On a mathematically foundational level, our most successful physical theories (gauge field theories and general-relativistic theories) are formulated in a framework based on the differential geometry of connections on principal bundles. After reviewing the essentials of this framework, we articulate the generalized hole and point-coincidence arguments, examining how they weight on a substantivalist position towards bundle spaces. This question, then, is considered in light of the Dressing Field Method, which allows a manifestly invariant reformulation of gauge field theories and general-relativistic theories, making their conceptual structure more transparent: it formally implements the point-coincidence argument and thus allows to define (dressed) fields and (dressed) bundle spaces immune to hole-type arguments.

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Philipp Berghofer, Jordan François, Lucrezia Ravera. 2026-07-21. What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers. https://doi.org/10.1007/s10701-026-00941-x

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