Ján Špakula :: papers and other works

Most of my papers have been arxived; the full list is below (together with links to arxiv or other places where a full text can be obtained). This page exists mostly to list some extra pieces – look for miscellaneous notes below.

papers :: preprints

• Boundary representations of hyperbolic groups: the log-Sobolev case, with Kevin Boucher, on arxiv
• Sobolev spaces and uniform boundary representations, with Kevin Boucher, on arxiv

published

• Measured asymptotic expanders and rigidity for Roe algebras, with Kang Li and Jiawen Zhang, in International Mathematics Research Notices, 2022, doi arxiv
• Measured expanders, with Kang Li and Jiawen Zhang, in Journal of Topology and Analysis, 2022, doi arxiv
• Quasi-local Algebras and Asymptotic Expanders, with Kang Li, Piotr Nowak, and Jiawen Zhang, in Groups, Geometry, and Dynamics, 2021, doi arxiv
• Quasi-locality and Property A, with Jiawen Zhang, in Journal of Functional Analysis, 2019, doi arxiv
• Relative commutant pictures of Roe algebras, with Aaron Tikuisis, in Communications in Mathematical Physics, 2019, doi arxiv
• Coarse medians and Property A, with Nick Wright, in Algebraic and Geometric Topology, 2018, doi arxiv
• A metric approach to limit operators, with Rufus Willett, in Transactions of AMS, 2017, doi arxiv
• Strong hyperbolicity, with Bogdan Nica, in Groups, Geometry and Dynamics, 2016, doi arxiv
• Uniform local amenability, with Jacek Brodzki, Graham Niblo, Rufus Willett, and Nick Wright, in Journal of Noncommutative Geometry, 2013, doi arxiv
• On rigidity of Roe algebras, with Rufus Willett, in Advances of Mathematics, 2013, doi arxiv
• Coarse non-amenability and coarse embeddings, with Goulnara Arzhantseva and Erik Guentner, in GAFA, 2012, doi (’The original publication is available at www.springerlink.com’) arxiv
• Maximal and reduced Roe algebras of coarsely embeddable spaces, with Rufus Willett, in Journal für die reine und angewandte Mathematik (Crelle’s Journal), 2012, doi arxiv
• Controlled coarse homology and isoperimetric inequalities, with Piotr Nowak, in Journal of Topology, 2010, pdf doi arxiv
• Non-K-exact uniform Roe C\*-algebras, in Journal of K-theory, 2012, pdf (Copyright held by Cambridge University Press) doi arxiv
• Uniform version of Weyl–von Neumann theorem, in Archiv der Mathematik, 2010, doi (’The original publication is available at www.springerlink.com’ link) arxiv
• Uniform K-homology, in Journal of Functional Analysis, 2009, pdf doi
• Almost homomorphisms of compact groups, with Pavol Zlatoš, in Illinois J. Math, 2004, pdf

miscellaneous notes

• A “straightforward” bilipschitz embedding of hyperbolic groups into ℓ¹ pdf.
  This is a construction of an embedding that mimics the usual proof for trees; however to make it directly work for a hyperbolic group one needs to use a “strongly hyperbolic” metric. (So, another one of the “strongly hyperbolic metric makes life easy”.)
• Metric Sparsification Property and limit operators pdf.
  This has been superseded by a paper with Rufus Willett [“A metric approach to limit operators”, on arxiv], which moreover generalises the notion of limit operators to a metric setting (as opposed to a group setting). I’m leaving this note up for anyone wanting to read the part “Property A implies that norms of inverses of limit ops are uniformly bounded” (i.e. a generalisation of Lindner and Seidel arxiv link to groups with Property A) in the group setting. This means that the machinery of ultralimits, limit spaces and such is not needed for this note; the notion of limit operators used is the “usual” one, a-la Rabinovich–Roch–Silbermann.
• pdf: A short note loosely explaining the argument of Ostrovskii [Low-distortion embeddings of graphs with large girth, JFA 2012] using our terminology [Arzhantseva-Guentner-S: Coarse non-amenability and coarse embeddings, GAFA 2012]. As Ostrovskii uses a very different notation from ours, I wanted to summarise the extra argument he does to get not only “coarsely embeddable”, but “bilipschitz into ℓ¹” space without Property A.

theses

• PhD thesis (may 2008; “K-theory of uniform Roe algebras”; Advisor Guoliang Yu; the content is mostly in the two papers “Uniform K-homology” and “Non-K-exact uniform Roe C*-algebras”) (pdf)
• Master thesis (july 2003; “On the locally compact case of Torunczyk’s Approximation theorem”; Advisor Jan J. Dijkstra) (pdf)
• Diploma thesis (in slovak) (june 2003; “Aplikácie neštandardnej analýzy”; Advisor P. Zlatoš) (pdf)