Cubical Homotopy Theory

Brian A. Munson is an Assistant Professor of Mathematics at the US Naval Academy. He has held postdoctoral and visiting positions at Stanford University, Harvard University, and Wellesley College, Massachusetts. His research area is algebraic topology, and his work spans topics such as embedding theory, knot theory, and homotopy theory. Ismar Volić is an Associate Professor of Mathematics at Wellesley College, Massachusetts. He has held postdoctoral and visiting positions at the University of Virginia, Massachusetts Institute of Technology, and Louvain-la-Neuve University in Belgium. His research is in algebraic topology and his articles span a wide variety of subjects such as knot theory, homotopy theory, and category theory. He is an award-winning teacher whose research has been recognized by several grants from the National Science Foundation.

• Preface; Part I. Cubical Diagrams: 1. Preliminaries; 2. 1-cubes: homotopy fibers and cofibers; 3. 2-cubes: homotopy pullbacks and pushouts; 4. 2-cubes: the Blakers-Massey Theorems; 5. n-cubes: generalized homotopy pullbacks and pushouts; 6. The Blakers–Massey Theorems for n-cubes; Part II. Generalizations, Related Topics, and Applications: 7. Some category theory; 8. Homotopy limits and colimits of diagrams of spaces; 9. Cosimplicial spaces; 10. Applications; Appendix; References; Index.

'… this volume can serve as a good point of reference for the machinery of homotopy pullbacks and pushouts of punctured n-cubes, with all the associated theory that comes with it, and shows with clarity the interest these methods have in helping to solve current, general problems in homotopy theory. Chapter 10, in particular, proves that what is presented here goes beyond the simple development of a new language to deal with old problems, and rather shows promise and power that should be taken into account.' Miguel Saramago, MathSciNet