Preprints and Classics 3: Resolutions, Context Free Groups, Hitchin Pairs

Some arXiv links:

  • Gwyneth R. Whieldon, Infinite Free Resolutions over Monomial Rings in Two Variables: Let $ k$ be a field. The author constructs an explicit free resolution of $ k$ over $ k[x,y]/M$ where $ M$ is a monomial ideal given by an explicit minimal generating set, and uses this to compute the Betti series of $ k$ over the $ k[x,y]/M$. This paper contains some nice examples.
  • Volker Diekert and Armin Weiß, Context-Free Groups and Bass-Serre Theory: This is a set of lecture notes at a summer school on automorphisms of free groups. Given a finitely presented group, we can consider the formal language in the generators and relations whose words are the identity, and the group is called context free if the language is context free. The authors illustrate the different characterisations of context free groups and the connections between them.
  • Eduardo Martínez-Pedroza and Daniel T. Wise, Coherence and Negative Sectional Curvature in Complexes of Groups: The authors, amongst other things, give a condition on a simply connected 2-complex so that any properly acting group is coherent (= finitely generated subgroups are finitely presented).
  • Małgorzata Stawiska, Lucjan Emil Böttcher (1872-1937)– the Polish pioneer of holomorphic dynamics: A summary of the work of the fellow in the title, who worked on iterations of holomorphic functions.
  • Goncalo Tabuada, Weil transfer of noncommutative motives: A noncommutative analogue of the Weil restriction on Chow motives to noncommutative motives.
  • Pierre-Henri Chaudouard and Gérard Laumon, Sur le comptage des fibrés de Hitchin nilpotents: The authors investigate the counting of Hitchin pairs on a projective curve and give some explicit formulaes for a restricted class of adelic integrals via the zeta function of the curve.

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