This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology.

This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology which took place in Arolla Switzerland from August 20-25 2012. The papers in this volume cover topics such as category theory and homological algebra functor homology algebraic $K$-theory cobordism categories group theory generalized cohomology theories and multiplicative structures the theory of iterated loop spaces Smith-Toda complexes and topological modular forms.

This volume contains the proceedings of the WIT: Women in Topology workshop, held from August 18-23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students. This volume contains papers based on the results obtained by team projects in homotopy theory, including $A$-infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological...