Topological Methods in Group Theory

Abstract

Introduction to Axiomatic Set Theory. 2nd ed. 2 OXTOBY. Measure and Category. 2nd ed. 3 SCHAEFER. Topological Vector Spaces. 2nd ed. 4 HILTON/STAMMBACH. A Course in Homological Algebra. 2nd ed. 5 MAC LANE. Categories for the Working Mathematician. 2nd ed. 6 HUGHES/PIPER. Projective Planes. 8 TAKEUTI/ZARING. Axiomatic Set Theory. 9 HUMPHREYS. Introduction to Lie Algebras and Representation Theory. 10 COHEN. A Course in Simple Homotopy Theory. 11 CONWAY. Functions of One Complex Variable I. 2nd ed. 12 BEALS. Advanced Mathematical Analysis. 13 ANDERSON/FULLER. Rings and Categories of Modules. 2nd ed. 14 GOLUBITSKY/GUILLEMIN. Stable Mappings and Their Singularities.

Curvature and Group Theory

“…With a little more technique this statement can be shown to remain true even if the G-action is not free, but merely proper, and if M 0 is merely homotopy equivalent (as is the case) to a finite complex. See Sections 17.5 and 17.6 of [5] for more details. Summarizing: Proposition 6.3.…”

“…A general reference for the material on CAT (0) geometry is [1]. All the other material discussed here is dealt with in full detail in my book [5], where original sources are also given.…”

“…Cohomology in dimension 2: What can be said about H 2 (G, ZG)? A theorem of Farrell (see [5] for a proof) says:…”

One-relator groups and proper 3-realizability

“…Recall that, given a compact 2-polyhedron K with π 1 (K) ∼ = G andK as its universal cover, the number of ends of G equals the number of ends ofK which in turn equals 0, 1, 2 or ∞ (see [17,31]). …”

“…Observe that, in general, if a group has infinitely many ends then Stallings' theorem tells us that it splits as an amalgamated free product or an HNN-extension over a finite group (see [31,17]), and Dunwoody's accessibility result [11] shows that the process of further factorization of the group in this way must terminate after a finite number of steps, and each of the factors can have at most one end. In the torsion-free case, the above translates into a decomposition of G into a free product of a free group with a one-relator group, the latter having at most one end.…”