8 papers · 1 filter
Instantons and rational homology spheres
Aliakbar Daemi, Mike Miller Eismeier
In previous work, the second author defined 'equivariant instanton homology groups' for a rational homology 3-sphere , a set of auxiliary data , and a PI…
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…
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…
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…
Handle decomposition complexity and representation spaces
Paolo Aceto, Aliakbar Daemi, Jennifer Hom +2
We prove that there are homology three-spheres that bound definite four-manifolds, but any such bounding four-manifold must be built out of many handles. The argument uses the homo…
Unoriented skein exact triangles in equivariant singular instanton Floer theory
Aliakbar Daemi, Christopher Scaduto
Equivariant singular instanton Floer theory is a framework that associates to a knot in an integer homology 3-sphere a suite of homological invariants that are derived from circle-…