Lectures on low-dimensional topology by K. Johannson, K. Johannson

By K. Johannson, K. Johannson

In the course of the week of may well 18-26, 1992, a convention on low-Dimensional Topology was once held on the college of Tennessee, Knoxville. The convention used to be dedicated to a vast spectrum of subject matters in Low-Dimensional Topology. in spite of the fact that, certain emphasis used to be given to hyperbolic and combinatorial buildings, minimum floor idea, negatively curbed teams, crew activities on R-trees, and gauge theoretic points of 3-manifolds. contemporary ends up in those themes are released the following. a different try used to be made to make this convention available and valuable for younger researchers within the box. This quantity is the main whole and present compilation of analysis within the box of Low-Dimensional Topology.

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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.

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. Chas M, Sullivan D (2004) Closed operators in topology leading to Lie bialgebras and higher string algebra. 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.

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