14 citations · 56 across the 22 of their papers we have counts for
24 papers
On symplectic aspects of character varieties for punctured surfaces
Aliakbar Daemi, Christopher Scaduto
For a surface with an odd number of punctures, the moduli space of flat connections with traceless holonomy around each puncture is a symplectic manifold. When the moduli s…
Instantons, indefinite 4-manifolds, and Dehn surgery
Aliakbar Daemi, Xingpei Liu, Mike Miller Eismeier
We prove that there exist hyperbolic integer homology spheres with arbitrarily large Dehn surgery number. Previously, no integer homology sphere was known to have a surgery number…
Nullhomotopic knots are determined by their complements
Aliakbar Daemi, Ciprian Manolescu, Tye Lidman +1
We prove that nullhomotopic knots in three-manifolds are determined by their complements. This answers a Kirby Problem posed by Boileau. The argument uses techniques in instanton F…
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…
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…
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-…
Rank three instantons, representations and sutures
Aliakbar Daemi, Nobuo Iida, Christopher Scaduto
We show that the knot group of any knot in any integer homology sphere admits a non-abelian representation into such that meridians are mapped to matrices whose eigenvalues…
Monotone Lagrangian Floer theory in smooth divisor complements: III
Aliakbar Daemi, Kenji Fukaya
This is the third paper in a series of papers studying intersection Floer theory of Lagrangians in the complement of a smooth divisor. We complete the construction of Floer homolog…
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 PID…
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…
Instantons, special cycles, and knot concordance
Aliakbar Daemi, Hayato Imori, Kouki Sato +2
We introduce a framework for defining concordance invariants of knots using equivariant singular instanton Floer theory with Chern-Simons filtration. It is demonstrated that many o…
3-manifolds without any embedding in symplectic 4-manifolds
Aliakbar Daemi, Tye Lidman, Mike Miller Eismeier
We show that there exist infinitely many closed 3-manifolds that do not embed in closed symplectic 4-manifolds, disproving a conjecture of Etnyre-Min-Mukherjee. To do this, we cons…
Lagrangians, SO(3)-instantons and mixed equation
Aliakbar Daemi, Kenji Fukaya, Maksim Lipyanskiy
The mixed equation, defined as a combination of the anti-self-duality equation in gauge theory and Cauchy-Riemann equation in symplectic geometry, is studied. In particular, regula…
Lagrangians, SO(3)-instantons and the Atiyah-Floer Conjecture
Aliakbar Daemi, Kenji Fukaya, Maksim Lipyanskiy
A version of the Atiyah-Floer conjecture, adapted to admissible SO(3)-bundles, is established.
Chern-Simons functional, singular instantons, and the four-dimensional clasp number
Aliakbar Daemi, Christopher Scaduto
Kronheimer and Mrowka asked whether the difference between the four-dimensional clasp number and the slice genus can be arbitrarily large. This question is answered affirmatively b…
Equivariant aspects of singular instanton Floer homology
Aliakbar Daemi, Christopher Scaduto
We associate several invariants to a knot in an integer homology 3-sphere using singular instanton gauge theory. There is a space of framed singular connections for such a…
Ribbon homology cobordisms
Aliakbar Daemi, Tye Lidman, David Shea Vela-Vick +1
We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homo…
Chern-Simons Functional and the Homology Cobordism Group
Aliakbar Daemi
For each integral homology sphere , a function on the set of integers is constructed. It is established that depends only on the homology cobordism of and it rec…
Monotone Lagrangian Floer theory in smooth divisor complements: II
Aliakbar Daemi, Kenji Fukaya
In the first part of the present series of papers, we studied the moduli spaces of holomorphic discs and strips into an open symplectic manifold, isomorphic to the complement of a…
Monotone Lagrangian Floer theory in smooth divisor complements: I
Aliakbar Daemi, Kenji Fukaya
In this paper, Floer homology for Lagrangian submanifolds in an open symplectic manifold given as the complement of a smooth divisor is discussed. The main new feature of this cons…
Surgery, Polygons and -Floer Homology
Lucas Culler, Aliakbar Daemi, Yi Xie
Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles…
Atiyah-Floer Conjecture: a Formulation, a Strategy to Prove and Generalizations
Aliakbar Daemi, Kenji Fukaya
Around 1988, Floer introduced two important theories: instanton Floer homology as invariants of 3-manifolds and Lagrangian Floer homology as invariants of pairs of Lagrangians in s…
Sutured Manifolds and Polynomial Invariants from Higher Rank Bundles
Aliakbar Daemi, Yi Xie
For each integer , Mariño and Moore defined generalized Donaldson invariants by the methods of quantum field theory, and made predictions about the values of these invaria…
Abelian Gauge Theory, Knots and Odd Khovanov Homology
Aliakbar Daemi
A homological invariant of 3-manifolds is defined, using abelian Yang-Mills gauge theory. It is shown that the construction, in an appropriate sense, is functorial with respect to…