20 citations · 52 across the 16 of their papers we have counts for
16 papers
Topological perspectives on the vanishing of some Bogomolov multipliers
Eric Samperton, Carlos Segovia
Since the 1980s, the Bogomolov multiplier of a finite group has been known to obstruct rationality in complex algebraic geometry, and more recently it is understood to be responsib…
Obstruction theory and the complexity of counting group homomorphisms
Eric Samperton, Armin Weiß
Fix a finite group . We study the computational complexity of counting problems of the following flavor: given a group , count the number of homomorphisms . Our first…
On the hardness of approximating minimum distances of quantum codes
Elena Grigorescu, Vatsal Jha, Eric Samperton
The problem of computing distances of error-correcting codes is fundamental in both the classical and quantum settings. While hardness for the classical version of these problems h…
An elementary proof that linking problems are hard
Shannon Cheng, Anna Chlopecki, Saarah Nazar +1
We give a new, elementary proof of what we believe is the simplest known example of a ``natural'' problem in computational 3-dimensional topology that is -hard -- name…
Towards a complexity-theoretic dichotomy for TQFT invariants
Nicolas Bridges, Eric Samperton
We show that for any fixed -dimensional TQFT over of either Turaev-Viro-Barrett-Westbury or Reshetikhin-Turaev type, the problem of (exactly) computing its inva…
An algorithm for Tambara-Yamagami quantum invariants of 3-manifolds, parameterized by the first Betti number
Colleen Delaney, Clément Maria, Eric Samperton
Quantum topology provides various frameworks for defining and computing invariants of manifolds inspired by quantum theory. One such framework of substantial interest in both mathe…
Topological quantum computation is hyperbolic
Eric Samperton
We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant of knots can always be arranged so that the knot diagrams with whi…
Oriented and unitary equivariant bordism of surfaces
Andrés Angel, Eric Samperton, Carlos Segovia +1
Fix a finite group . We study and , the unitary and oriented bordism groups of smooth -equivariant compact surfaces, respectively, and we calculate th…
Free actions on surfaces that do not extend to arbitrary actions on 3-manifolds
Eric Samperton
We provide the first known example of a finite group action on an oriented surface that is free, orientation-preserving, and does not extend to an arbitrary (in particular, pos…
Coloring invariants of knots and links are often intractable
Greg Kuperberg, Eric Samperton
Let be a nonabelian, simple group with a nontrivial conjugacy class . Let be a diagram of an oriented knot in , thought of as computational input. We sh…
Haah codes on general three manifolds
Kevin T. Tian, Eric Samperton, Zhenghan Wang
Haah codes represent a singularly interesting gapped Hamiltonian schema that has resisted a natural generalization, although recent work shows that the closely related type I fract…
Computational Complexity of Enumerative 3-Manifold Invariants
Eric Samperton
Fix a finite group . We analyze the computational complexity of the problem of counting homomorphisms , where is a topological space treated as computational i…
Schur-type invariants of branched G-covers of surfaces
Eric Samperton
Fix a finite group and a conjugacy invariant subset . Let be an oriented surface, possibly with punctures. We consider the question of when two homomorphisms…
Computational complexity and 3-manifolds and zombies
Greg Kuperberg, Eric Samperton
We show the problem of counting homomorphisms from the fundamental group of a homology -sphere to a finite, non-abelian simple group is #P-complete, in the case that …
Spaces of invariant circular orders of groups
Hyungryul Baik, Eric Samperton
Motivated by well known results in low-dimensional topology, we introduce and study a topology on the set CO(G) of all left-invariant circular orders on a fixed countable and discr…
On laminar groups, Tits alternatives, and convergence group actions on
Juan Alonso, Hyungryul Baik, Eric Samperton
Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certai…