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math.GT2025
The knot complement problem for null-homotopic knots
Aliakbar Daemi, Tye Lidman
We prove that for three-manifolds satisfying a certain algebraic condition on their fundamental group, null-homotopic knots are determined by their complements. This answers a Kirb…
math.GT2025
Filtered instanton homology and cosmetic surgery
Aliakbar Daemi, Mike Miller Eismeier, Tye Lidman
The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two different Dehn surgeries results in distinct oriented three-manifolds. Hans…
math.GT2025
The mapping class group action on the odd character variety is faithful
Aliakbar Daemi, Christopher Scaduto
The odd character variety of a Riemann surface is a moduli space of SO(3) representations of the fundamental group which can be interpreted as the moduli space of stable holomorphi…