11 papers
Strongly explicit Ramanujan 2-lift towers via Hilbert modular forms
Olga Kharlampovich, Igor Pak, Alina Vdovina
Expander graphs have been central objects of study for over fifty years. Ramanujan graphs attain the asymptotically optimal nontrivial adjacency-eigenvalue threshold for infinite f…
Aleshin graphs are expanders
Olga Kharlampovich, Alina Vdovina
We prove that the Aleshin level graphs are two-sided expanders. We establish linear diameter bounds for Belaterra and Aleshin graph families. At level , the diameters of the Bel…
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…
Real and complex K-theory for higher rank graph algebras arising from cube complexes
Jeffrey L Boersema, Alina Vdovina
Using the Evans spectral sequence and its counter-part for real -theory, we compute both the real and complex -theory of several infinite families of -algebras based on…
Generalizations of free monoids
M. V. Lawson, A. Vdovina
We generalize free monoids by defining -monoids. These are nothing other than the one-vertex higher-rank graphs used in -algebra theory with the cardinality requiremen…
Quantifying separability in RAAGs via representations
Olga Kharlampovich, Alina Vdovina
We answer the question asked by Louder, McReynolds and Patel, and prove the following statement. Let L be a RAAG, H a word quasiconvex subgroup of L, then there is a finite dimensi…