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

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a broadening of vistas, a synergy among once-differentiated topics, and ideas to mathematical difficulties either outdated and new.

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Whitehead, On the 3-type of a complex, Proc. Nat. Acad. Sci. 36 (1950), 41–48. 23. J. P. May, The Geometry of Iterated Loop Spaces, Lecture Notes in Mathematics 271, Springer, Berlin, 1972. 24. J. P. May, Classifying spaces and fibrations, Mem. Amer. Math. Soc. 1 (1975), no. 155. 25. R. J. Milgram, The bar construction and abelian -spaces, Illinois J. Math. 11 (1967), 242–250. 26. J. Milnor, Construction of universal bundles II, Ann. Math. 63 (1956), 430–436. 27. I. -A. Svensson, Algebraic classification of equivariant homotopy 2-types, part I, J.

A smooth, compact category C is said to be a “Morse–Smale” category if the following additional properties are satisfied: ÅÓÖº » ÅÓÖº » ÅÓÖº » ÅÓÖº » 1. The objects of C are partially ordered by the condition if ÅÓÖº » ÅÓÖº » 2. identity . 3. There is a set map, Ï that if , Ç ºC » Z, which preserves the partial ordering, such Ñ ÅÓÖº » º » º » ½ The map is known as an “index” map. A Morse–Smale category such as this is said to have finite type, if there are only finitely many objects of any given index, and for each pair of objects , there are only finitely many objects with .

2. J. C. Baez, A. S. Crans, U. Schreiber and D. Stevenson, From loop groups to 2-groups, HHA 9 (2007), 101–135. Also available as arXiv:math/0504123. 3. J. C. Baez and A. Lauda, Higher-dimensional algebra V: 2-groups, Th. Appl. Cat. 12 (2004), 423–491. Also available as arXiv:math/0307200. 4. J. C. Baez and U. Schreiber, Higher gauge theory, in Categories in Algebra, Geometry and Mathematical Physics, eds. A. , Contemp. Math. 431, AMS, Providence, RI, 2007, pp. 7–30. Also available as arXiv:math/0511710.