9 papers
Weak Factorization and Product Systems Over Groupoids
Jon Bannon, Alina Vdovina
We give a product-system description of generalized higher-rank graphs with the weak factorization property. For such a graph with degree-zero groupoid G, we prove that weak factor…
Equations in Products of Free Groups and 3-Manifold Groups II: Olshanskii Epimorphisms
Olga Kharlampovich, Alina Vdovina
In 1989 Olshanskii introduced a three-parameter family of coordinate-surjective homomorphisms from the genus-two surface group to a direct product of two rank-two free groups. When…
Equations in Products of Free Groups and 3-Manifold Groups, I
Olga Kharlampovich, Alina Vdovina
Perelman's proof of the Poincare conjecture shows that every simply connected closed 3-manifold is homeomorphic to the 3-sphere. The fundamental groups of 3-manifolds attract lots…
Ramanujan subshifts
Ievgen Bondarenko, Rostislav Grigorchuk, Alina Vdovina
A finite, connected, -regular graph is called Ramanujan if every its eigenvalue satisfies either or . The Ramanujan condition corres…
Seifert-Tait graphs
Stephen Huggett, Alina Vdovina
We show that among alternating knots, those which have diagrams whose Seifert and Tait graphs are isomorphic are dominant.
Simplicity of -algebras of contracting self-similar groups
Eusebio Gardella, Volodymyr Nekrashevych, Benjamin Steinberg +1
We show that the -algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex -algebra is simple. We also i…