Free loopspaces and equivariant classifying spaces
Copyright policy )Free loopspaces and equivariant classifying spaces
For \(\pi\) a discrete group, \(X\) a classifying space for \(\pi\), SO(2) the topological group of rotations of the plane about the origin and \({\mathcal C}_k\) the cyclic subgroup with \(k\) elements, \({\mathcal C}_k\subset \text{SO}(2)\), the author gives a group-theoretic description of the \({\mathcal C}_k\)-equivariant homotopy type of the path components of \(\Lambda X\) (the free loop space). The results of this paper will be used, in a preprint, for counting periodic orbits of identity maps of \(\pi\)-spaces. Thus the author obtains invariants of the algebraic K-theory of the classifying space of a finite group.
- University of Illinois System United States
- University of Illinois at Urbana–Champaign United States
Simplicial sets and complexes in algebraic topology, algebraic K-theory, Classifying spaces of groups and \(H\)-spaces in algebraic topology, Eilenberg-Mac Lane spaces, Classification of homotopy type, Equivariant homotopy theory in algebraic topology
Simplicial sets and complexes in algebraic topology, algebraic K-theory, Classifying spaces of groups and \(H\)-spaces in algebraic topology, Eilenberg-Mac Lane spaces, Classification of homotopy type, Equivariant homotopy theory in algebraic topology
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