By John C. Baez, Danny Stevenson (auth.), Nils Baas, Eric M. Friedlander, Björn Jahren, Paul Arne Østvær (eds.)

ISBN-10: 3642011993

ISBN-13: 9783642011993

The 2007 Abel Symposium came about on the college of Oslo in August 2007. The aim of the symposium was once to compile mathematicians whose study efforts have resulted in fresh advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. a typical subject of this symposium used to be the advance of latest views and new buildings with a specific taste. because the lectures on the symposium and the papers of this quantity display, those views and structures have enabled a broadening of vistas, a synergy among once-differentiated topics, and recommendations to mathematical difficulties either previous and new.

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Classes of maps ¼ ¢ and Proof that In effect, we are studying free homotopy ¢ where is the closed surface of genus and is a graph whose first homology has rank . Then a map ¼ extends to if and only if ¼ sends to the identity. Any two extensions are homotopic because ¢ has contractible universal cover. Writing as ¼ union a two-disk we see any nontrivial embedded closed curve in can be isotoped into ¼ giving a nontrivial embedded curve distinct from the boundary. Conversely, if a nontrivial embedded curve on the surface with boundary is not freely homotopic to the boundary then it is still nontrivial in the closed surface.

The legacy of Niels Henrik Abel, pp 771–784. GT] 11. Sullivan D Open and closed string topology. In: Graeme Segal 60th Proceedings 12. Abbaspour H (2005) On string topology of 3-manifolds. Topology 44(5):1059–1091. arXiv:0310112 13. Etingof P (2006) Casimirs of the Goldman Lie algebra of a closed surface. Int Math Res Not Floer Homotopy Theory, Realizing Chain Complexes by Module Spectra, and Manifolds with Corners Ralph L. Cohen Abstract In this paper we describe and continue the study begun in Cohen et al.

D. Quillen, Higher algebraic K-theory I, in Algebraic -theory, I: Higher -theories (Proc. , 1972), Lecture Notes in Mathematics, 341, Springer, Berlin, 1973, pp. 85–147. Ò Ò Ò ½ Ä À Ã Ã The Classifying Space of a Topological 2-Group Ä 31 29. H. Sati, J. Stasheff and U. Schreiber, ½ -algebra connections and applications to String– and Chern–Simons -transport, to appear in the proceedings of Recent Developments in Quantum Field Theory, Max Planck Institute. 3480. 30. U. D. thesis, U. Essen. Available as arXiv:hep-th/0509163.

### Algebraic Topology: The Abel Symposium 2007 by John C. Baez, Danny Stevenson (auth.), Nils Baas, Eric M. Friedlander, Björn Jahren, Paul Arne Østvær (eds.)

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