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This is a Quantitative Study study.

October 20, 2025Open Access

Homology lens spaces and SL(2,C)

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Irreducible representations of π1(Y) in SL(2,C) exist for many closed oriented 3-manifolds.
The main condition for Y is H1(Y;Z) having order less than 5, excluding S^3 and lens spaces.
This study focuses on the case where H1(Y;Z) is isomorphic to Z/4Z, utilizing advanced techniques.
These findings could illuminate the connections between topology and representation theory.

Implication

Research reveals irreducible representations of π1(Y) in SL(2,C) for specific homology structures, indicating geometric constraints.

Abstract

We prove that if Y is a closed, oriented 3-manifold with first homology H₁(Y;Z) of order less than $5$, then there is an irreducible representation π₁(Y) → SL(2,C) unless Y is homeomorphic to S³, a lens space, or RP³ # RP³. By previous work it suffices to consider the case H₁(Y;Z) Z/4Z, which we accomplish using holonomy perturbation techniques in instanton Floer homology.

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Cite This Study

Ghosh et al. (2025) studied this question.

synapsesocial.com/papers/68f5fcce8d54a28a75cf1db4 https://doi.org/10.48550/arxiv.2509.25019

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Implication

Research reveals irreducible representations of π1(Y) in SL(2,C) for specific homology structures, indicating geometric constraints.

Homology lens spaces and SL(2,C)

Key Points

Implication

Abstract

Discussion

Cite This Study

Homology lens spaces and SL(2,C)

Key Points

Implication

Abstract

Discussion

Cite This Study

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