Mundet i Riera, IgnasiCarol Raventós2025-06-122025-06-122025-01-15https://hdl.handle.net/2445/221497Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Ignasi Mundet i RieraThis work investigates the classification of $\mathbb{Z}_p$-manifolds, compact (pathconnected) Riemannian manifolds whose holonomy group is isomorphic to $\mathbb{Z}_p$, up to affine equivalence. It uses the foundational results of Bieberbach groups and cohomological methods to achieve two primary objectives: classifying affine equivalence classes of $\mathbb{Z}_p$-manifolds and analyzing the case where non-homotopic $\mathbb{Z}_p$-manifolds become affinely equivalent when taking the product by $S^1$. This work also provides a way to find pairs of such non-homotopic $\mathbb{Z}_p$-manifolds that become isomorphic after taking Cartesian product by $S^1$. Notation: In this work, $\mathbb{Z}_p$ refers to $\mathbb{Z} / p \mathbb{Z}$, where $p \in \mathbb{Z}, p \neq 0$.65 p.application/pdfengcc-by-nc-nd (c) Gerard Carol Raventós, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/es/Geometria diferencialVarietats de RiemannHomologiaTreballs de fi de grauDifferential geometryRiemannian manifoldsHomologyBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess