This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009.

This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology.

In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.

Readership

Graduate students and research mathematicians interested in properties of function spaces.

Table of Contents

• S. B. Smith -- The homotopy theory of function spaces: A survey

• U. Buijs -- Upper bounds for the Whitehead-length of mapping spaces
• D. Chataur -- String topology of classifying spaces and gravity algebras
• M. C. Crabb -- A fibrewise stable splitting and free loops on projective spaces
• Y. Félix and D. Tanré -- Rational homotopy of symmetric products and spaces of finite subsets
• J.-B. Gatsinzi -- Derivations, Hochschild cohomology and the Gottlieb group
• J.-B. Gatsinzi and R. Kwashira -- Rational homotopy groups of function spaces
• J. Giansiracusa and P. Salvatore -- Formality of the framed little 2-discs operad and semidirect products
• M. Golasiński, D. Gonçalves, and P. Wong -- James construction, Fox torus homotopy groups and Hopf invariants
• A. Kono and S. Tsukuda -- Notes on the triviality of adjoint bundles
• A. Kozlowski and K. Yamaguchi -- Spaces of algebraic maps from real projective spaces into complex projective spaces
• K. Kuribayashi -- On the rational cohomology of the total space of the universal fibration with an elliptic fibre
• J. Oprea and J. Strom -- On the realizability of Gottlieb groups
• C. L. Schochet and S. B. Smith -- Localization of grouplike function and section spaces with compact domain
• C. Wockel -- Non-integral central extensions of loop groups

• Y. Félix -- Problems on mapping spaces and related subjects