The Bredon–Löffler Conjecture
نویسندگان
چکیده
Greenlees thanks the University of She eld for URF grant number RSG/339. The large commutative diagrams in this article were typeset using Paul Taylor's diagram package. We give a brief exposition of results of Bredon and others on passage to fixed points from stable C2 equivariant homotopy (where C2 is the group of order two) and its relation to Mahowald’s root invariant. In particular we give Bredon’s easy equivariant proof that the root invariant doubles the stem; the conjecture of the title is equivalent to the Mahowald–Ravenel conjecture that the root invariant never more than triples the stem. Our main result is to verify by computation that the algebraic analogue of this holds in an extensive range: this improves on results of [Mahowald and Shick 1983].
منابع مشابه
Cohomological Finiteness Conditions in Bredon Cohomology
We show that soluble groups G of type Bredon-FP∞ with respect to the family of all virtually cyclic subgroups of G are always virtually cyclic. In such a group centralizers of elements are of type FP∞. We show that this implies the group is polycyclic. Another important ingredient of the proof is that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic ...
متن کاملSteenrod ∪ i - products on Bredon – Illman cohomology
Let G be a topological group acting on a space X. We construct a family of Steenrod’s ∪i -product [Ann. of Math. (2) 48 (1947) 290] on the Bredon–Illman cochain complex of X [Quart. J. Math. Oxford Ser. (2) 47 (1996) 199]. As corollaries, we get the existence of Steenrod squares on Bredon– Illman cohomology with appropriate coefficients as well as the triviality of the Gerstenhaber bracket indu...
متن کاملFixed Points of Finite Groups Acting on Generalised Thompson Groups
We study centralisers of finite order automorphisms of the generalised Thompson groups Fn,∞ and conjugacy classes of finite subgroups in finite extensions of Fn,∞. In particular we show that centralisers of finite automorphisms in Fn,∞ are either of type FP∞ or not finitely generated. As an application we deduce the following result about the Bredon type of such finite extensions: any finite ex...
متن کاملBredon Equivariant Homology of Representation Spheres
In this paper we compute the Bredon equivariant homology of representation spheres corresponding to the orientable three dimensional representations of cyclic groups and dihedral groups, as well as the symmetric group on three letters equipped with a permutation representation. These computations are greatly simplified by the introduction of a splitting theorem for the Burnside ring Mackey func...
متن کاملFrankl's Conjecture for a subclass of semimodular lattices
In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices ha...
متن کامل