Geodesic
Small Heegaard genus and SU(2)
Baldwin, John A1 ; Sivek, Steven2
1Department of Mathematics, Boston College, Chestnut Hill, MA, United States
2Department of Mathematics, Imperial College London, London, United Kingdom
Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2369-2390
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Let Y be a closed, orientable 3-manifold with Heegaard genus 2. We prove that if H1(Y ; ℤ) has order 1, 3, or 5, then there is a representation π1(Y ) → SU ⁡ (2) with nonabelian image. Similarly, if H1(Y ; ℤ) has order 2 then we find a nonabelian representation π1(Y ) → SO ⁡ (3). We also prove that a knot K in S3 is a trefoil if and only if there is a unique conjugacy class of irreducible representations π1(S3 ∖ K) → SU ⁡ (2) sending a fixed meridian to diag ⁡ (i,−i).

DOI : 10.2140/agt.2025.25.2369
Keywords: 3-manifolds, character varieties, SU(2)-simple knots, instanton Floer homology

Baldwin, John A  1   ; Sivek, Steven  2

1 Department of Mathematics, Boston College, Chestnut Hill, MA, United States
2 Department of Mathematics, Imperial College London, London, United Kingdom 
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Baldwin, John A; Sivek, Steven. Small Heegaard genus and SU(2). Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2369-2390. doi: 10.2140/agt.2025.25.2369

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