Igor Mineyev's links and comments on geometric group theory

• Magnus, Karras, Solitar. Combinatorial group theory.
• Lyndon, Schupp. Combinatorial group theory.
• John Meier. Groups, graphs and trees: an introduction to the geometry of infinite groups.
• Bridson, Haefliger. Metric spaces of non-positive curvature.
• Colins, Grigorchuk, Kurchanov, Zieschang. Combinatorial group theory and applications to geometry.
• Gersten (editor). Essays in group theory. MSRI publications.
• Ghys, de la Harpe. Sur les groupes hyperboliques d'apres Mikhael Gromov. Here is the english translation.
• Bedford, Keane, Series (editors). Ergodic theory, symbolic dynamics and hyperbolic spaces.
• Pierre de la Harpe. Topics in geometric group theory.
• Cornelia Drutu, Michael Kapovich. Geometric group theory.
• Survey on geometric group theory by Wolfgang Lueck. Here is the direct link to pdf file.
• Clara Loeh. Geometric group theory.

Books and links relating geometric group theory to algebra:

• See any link below mentioning groups.
• The IML project that I am running starting in Spring 2024: ColorTaiko!. The fun game that we will create in that project is secretly related to several long-standing open problems about group algebras called Kaplansky conjectures. My article showing the connection between the Kaplansky conjectures and the ColorTaiko! game will appear at some point on my website.
• Kenneth Brown. Cohomology of groups.
• My two papers giving a characterization of hyperbolic groups in terms of bounded cohomology: from hyperbolicity to bounded cohomology and from bounded cohomology to hyperbolicity.
• Wolfgang Lueck. L2-Invariants: Theory and Applications to Geometry and K-Theory (The definition of l^2-cohomology in terms of the von Neumann algebra of a group.)

• A great review of the models for the standard hyperbolic space:
  Hyperbolic geometry by Cannon, Floyd, Kenyon, Parry.
• Ghys, Haefliger, Verjovsky. Group theory from a geometrical viewpoint.
• Bridson, Haefliger. Metric spaces of non-positive curvature.
• Ken'ichi Ohshika. Discrete groups.
• Ilya Kapovich, Nadia Benakli. Boundaries of hyperbolic groups.
• My articles about conformal structures on the boundaries of hyperbolic groups, and about flows and joins of metric spaces (a generalization of the unit tangent bundle to general metric spaces).
• Michael Davis. The geometry and topology of Coxeter groups.
• Coornaert, Delzant, Papadopoulos. Géométrie et théorie des groupes.

• John Stallings. Topology of finite graphs. Invent. Math. 71. (1983), pages 551-565.
• My three papers on the strengthened Hanna Neumann conjecture and its generalizations. It is best to read them in the order opposite to the chronological oder, like this:
  paper 1: Groups, graphs, and the Hanna Neumann Conjecture (proves SHNC, this one is about free groups and graphs - one-dimensional),
  paper 2: Submultiplicativity and the Hanna Neumann Conjecture (proves SHNC and gives an analytic generalization of the statement of SHNC using l^2 Betti numbers),
  paper 3: The topology and analysis of the Hanna Neumann Conjecture (gives analytic generalizations of the statement of SHNC to higher-dimensional complexes).
• Hog-Angeloni, Metzler, Sieradski (editors). Two-dimensional homotopy and combinatorial group theory. London Mathematical Society Lecture Note Series, 197.
• Open problems in low-dimensional topology. (This is mostly about 2-dimensional questions.)
• John Hempel. 3-manifolds. (Obviously, 3-dimensional).
• Burde, Zieschang, Heusener. Knots.
• Dale Rolfsen. Knots and links. (Knot complements are 3-dimensional manifolds.)
• Cubical complexes (and their fundamental groups) play an important role in recent important developments in 3-dimensional topology. (References to appear.)

• Scott, Wall. Topological methods in group theory.
• Ross Geoghegan. Topological methods in group theory.
• Daniel Cohen. Combinatorial group theory: a topological approach.

• Wolfgang Lueck. L2-Invariants: Theory and Applications to Geometry and K-Theory (About Murray-von Neumann dimension, l^2 Betti numbers, the Atiyah problem, etc.)
• My paper 2 and paper 3 mentioned above that generalize the statement of strengthened Hanna Neumann conjecture in analytic terms (submultiplicativity).
• Piotr Nowak and Guoliang Yu. Large scale geometry. EMS Textbooks in Mathematics. European Mathematical Society (EMS). (About amenability, Yu's property A, etc.)
• Is Thompson's group amenable?
• Analysis on metric spaces (ideal boundaries of hyperbolic groups) have been tried to tackle Cannon's conjecture (still open).

• Epstein (editor), Cannon, Holt, Levy, Paterson, Thurston. Word processing in groups. (Automata, automatic groups, biautomatic groups, ...)
• Baumslag, Miller (editors). Algorithms and classification in combinatorial group theory. (A collection of articles on decision problems in groups, automatic groups, etc.)
• There is a relation between geometric group theory, music and artificial intelligence.
  • Musimathics, The Mathematical Foundations of Music, by Gareth Loy. This book is not directly about geometric group theory, but it is an introduction to the mathematics and physics of music, the intersection of art and science.
  • Orbit Computation for Atomically Generated Subgroups of Isometries of Z^n. Here is the preprint version of that paper.
  • A group-theoretic approach to computational abstraction: symmetry-driven hierarchical clustering.

• Dirichlet characters form a group under pointwise multiplication.
• Modular forms use subgroups of SL(2,Z) in their definition, acting on the upper-half-plane (= the hyperbolic plane). Tell me more about the role groups play in number theory.
• You might also enjoy my 11-minite meditative video related to number theory. Use Safari or Chrome. Firefox might not show this properly. Make it full-screen. Can you guess what this video represents?

• Open problems in low-dimensional topology.
• Open problems in combinatorial and geometric group theory.
• Questions in geometric group theory by Mladen Bestvina.
• Problems on boundaries of groups and kleinian groups by Misha Kapovich.
• Unsolved problems in algebra.
• Unsolved problems in group theory.