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 was once to compile mathematicians whose learn efforts have ended in contemporary advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. a standard subject of this symposium was once the advance of recent views and new structures with a specific style. because the lectures on the symposium and the papers of this quantity exhibit, 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broadening of vistas, a synergy among once-differentiated matters, and suggestions to mathematical difficulties either outdated and new.

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**Extra resources for Algebraic Topology: The Abel Symposium 2007**

**Sample text**

L. A. Baas et al. L. Cohen to exist by the author in [4], and it was calculated to be the stable homotopy type of the free loop space, . These were the results reported on by the author at the Abel conference in Oslo. In this largely expository note, we discuss basic notions of Floer homotopy type, and generalize them to discuss obstructions to the existence of a Floer £ -homology theory, when £ is a generalized cohomology theory. R, defined on an In a “Floer theory” one typically has a functional, A Ï Y infinite dimensional manifold, Y, whose critical points generate a “Floer chain complex”, £ A A .

Let us denote this space by G. This is the classifying space used by Jurˇco and Baas–B¨okstedt–Kro. It should be noted that the assumption that G is a well-pointed 2-group ensures that the nerve of the 2-groupoid G is a “good” simplicial space in the sense of Segal; this “goodness” condition is important in the work of Baas, B¨okstedt and Kro [1]. Baas, B¨okstedt and Kro also consider a third way to construct a classifying space for G. If we take the nerve G of G we get a simplicial group, as described in Sect.

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