More examples of discrete co-compact group actions
We survey some results and questions about free actions of infinite groups on products of spheres and euclidean spaces, and give some new co-compact examples.
math.GT↗
arXiv subjects
Erik K. Pedersen
Publications and source records attributed to Erik K. Pedersen.
Stability in controlled L-theory
We prove a squeezing/stability theorem for delta-epsilon controlled L-groups when the control map is a fibration on a finite polyhedron. A relation with boundedly-controlled L-groups is also discussed.
math.GT↗
Assembly Maps for Group Extensions in $K$-Theory and $L$-Theory with Twisted Coefficients
In this paper we show that the Farrell-Jones isomorphism conjectures are inherited in group extensions for assembly maps in algebraic $K$-theory and $L$-theory with twisted coefficients.
math.KT↗
Topological Equivalence of Linear Representations for Cyclic Groups, I & II
In the two parts of this paper we solve a problem of De Rham, proving that Reidemeister torsion invariants determine topological equivalence of linear G-representations, for G a finite cyclic group. Methods in controlled K-theory and surgery theory are developed to establish, and effectively calculate, a necessary and sufficient condition for non-linear similarity in terms of the vanishing of certain non-compact transfer maps. For cyclic groups of 2-power order, we obtain a complete classification of non-linear similarities.
math.GT↗
A finite loop space not rationally equivalent to a compact Lie group
We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.
math.AT↗