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

The 2007 Abel Symposium came about on the college of Oslo in August 2007. The aim of the symposium used to be to compile mathematicians whose study efforts have resulted in fresh advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. a typical topic of this symposium was once the improvement of recent views and new structures with a express taste. because the lectures on the symposium and the papers of this quantity reveal, those views and structures have enabled a broadening of vistas, a synergy among once-differentiated matters, and suggestions to mathematical difficulties either outdated and new.

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Ann Sci Ecol Norm 4 Suppl 24(6):635–704 4. Jaco W (1969) Heegaard splittings and splitting homomorphisms. Trans Am Math Soc 144:365–379 5. Stallings JR (1966) How not to prove the Poincar´e conjecture. Topology Seminar, Wisconsin, 1965. In: Bing RH, Bean RJ (eds) Annals of mathematics studies, vol 60. Princeton University Press, Princeton, pp 83–88 6. GT] 7. GT] 8. Chas M, Krongold F (work in progress) 9. Chas M (2004) Combinatorial Lie bialgebras of curves on surfaces. Topology 43:543–568. GT] 10.

Let denote the linear span of the classes of ¾ that are sent by to the trivial class in ¢ . Let denote the group ring of the kernel of the homomorphism ¢ induced by . ¾ × × × × × Ã Â Ã × × Î Proposition. is a subLie algebra of the Goldman Lie algebra . For the natural String Topology action of on the group ring of ¾ by derivations [11], keeps invariant. Î Â Ã Proof. The connected sum at an intersection point of a disk on a generator of and a disk on , a generator of is a disk on that term of the action of on .

Ginot, comment on U. Schreiber’s post Lie -connections and their application to stringand Chern–Simons -transport, -Category Caf´e. 16. G. Ginot and M. Stienon, Groupoid extensions, principal 2-group bundles and characteristic classes. 1238. 17. J. Giraud, Cohomologie Non Ab´elienne, Die Grundlehren der mathematischen Wissenschaften 179, Springer, Berlin, 1971. 18. A. Henriques, Integrating ½ -algebras. Available as arXiv:math/0603563. 19. J. F. Jardine, Universal Hasse–Witt classes, Contemp. Math.