Abstract
Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homological conformal field theory. This means in particular that it admits operations parameterized by homology classes of classifying spaces of diffeomorphism groups of surfaces. Here we present a radical extension of this result, giving a new construction in which diffeomorphisms are replaced with homotopy equivalences, and surfaces with boundary are replaced with arbitrary spaces homotopy equivalent to finite graphs. The result is a novel kind of field theory which is related to both the diffeomorphism groups of surfaces and the automorphism groups of free groups with boundaries. Our work shows that the algebraic structures in string topology of classifying spaces can be brought into line with, and in fact far exceed, those available in string topology of manifolds. For simplicity, we restrict to the characteristic 2 case. The generalization to arbitrary characteristic will be addressed in a subsequent paper.
Original language  English 

Pages (fromto)  394507 
Number of pages  114 
Journal  Advances in Mathematics 
Volume  281 
Early online date  29 May 2015 
DOIs  
Publication status  Published  20 Aug 2015 
Keywords
 string topology
 field theories
 classifying spaces
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Profiles

Richard Hepworth
 School of Natural & Computing Sciences, Mathematical Science  Senior Lecturer
 Mathematical Sciences (Research Theme)
Person: Academic