Homotopy theory of function spaces and related topics. Proceedings of the Oberwolfach workshop, Mathematisches Forschungsinstitut Oberwolfach, Germany, April 5–11, 2009.

*(English)*Zbl 1194.55003
Contemporary Mathematics 519. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4929-3/pbk). xi, 230 p. (2010).

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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.

The articles of this volume will be reviewed individually.

Indexed articles:

Smith, Samuel Bruce, The homotopy theory of function spaces: A survey, 3-39 [Zbl 1208.55006]

Buijs, Urtzi, Upper bounds for the Whitehead-length of mapping spaces, 43-53 [Zbl 1227.55008]

Chataur, David, String topology of classifying spaces and gravity algebras, 55-65 [Zbl 1213.55008]

Crabb, M. C., A fibrewise stable splitting and free loops on projective spaces, 67-75 [Zbl 1211.55005]

Félix, Yves; Tanré, Daniel, Rational homotopy of symmetric products and spaces of finite subsets, 77-92 [Zbl 1215.55004]

Gatsinzi, J.-B., Derivations, Hochschild cohomology and the Gottlieb group, 93-104 [Zbl 1221.55013]

Gatsinzi, J.-B.; Kwashira, R., Rational homotopy groups of function spaces, 105-114 [Zbl 1216.55003]

Giansiracusa, Jeffrey; Salvatore, Paolo, Formality of the framed little 2-discs operad and semidirect products, 115-121 [Zbl 1209.18008]

Golasiński, Marek; Gonçalves, Daciberg; Wong, Peter, James construction, Fox torus homotopy groups, and Hopf invariants, 123-132 [Zbl 1223.55006]

Kono, Akira; Tsukuda, Shuichi, Notes on the triviality of adjoint bundles, 133-144 [Zbl 1209.55004]

Kozlowski, Andrzej; Yamaguchi, Kohhei, Spaces of algebraic maps from real projective spaces into complex projective spaces, 145-164 [Zbl 1209.55005]

Kuribayashi, Katsuhiko, On the rational cohomology of the total space of the universal fibration with an elliptic fibre, 165-179 [Zbl 1227.55010]

Oprea, John; Strom, Jeff, On the realizability of Gottlieb groups, 181-188 [Zbl 1209.55007]

Schochet, Claude L.; Smith, Samuel B., Localization of grouplike function and section spaces with compact domain, 189-202 [Zbl 1214.55010]

Wockel, Christoph, Non-integral central extensions of loop groups, 203-214 [Zbl 1219.22018]

Félix, Yves, Problems on mapping spaces and related subjects, 217-230 [Zbl 1208.55007]

##### MSC:

55-06 | Proceedings, conferences, collections, etc. pertaining to algebraic topology |

55Pxx | Homotopy theory |

55Q52 | Homotopy groups of special spaces |

46M20 | Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) |

00B25 | Proceedings of conferences of miscellaneous specific interest |

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\textit{Y. Félix} (ed.) et al., Homotopy theory of function spaces and related topics. Proceedings of the Oberwolfach workshop, Mathematisches Forschungsinstitut Oberwolfach, Germany, April 5--11, 2009. Providence, RI: American Mathematical Society (AMS) (2010; Zbl 1194.55003)

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