The Equivariant Slice Filtration: a Primer
نویسنده
چکیده
We present an introduction to the equivariant slice filtration. After reviewing the definitions and basic properties, we determine the sliceconnectivity of various families of naturally arising spectra. This leads to an analysis of pullbacks of slices defined on quotient groups, producing new collections of slices. Building on this, we determine the slice tower for the Eilenberg-Mac Lane spectrum associated to a Mackey functor for a cyclic p-group. We then relate the Postnikov tower to the slice tower for various spectra. Finally, we pose a few conjectures about the nature of slices and pullbacks.
منابع مشابه
On the slice spectral sequence
We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is concentrated over a normal subgroup is related to the slice filtration of its geometric fixed points, and use this to prove a conjecture of Hill on the slice filtra...
متن کاملA Characterization of the Murasugi Polynomial of an Equivariant Slice Knot
We characterize the Murasugi polynomial of an equivariant slice knot by proving a conjecture of J. Davis and S. Naik. A knot K in S is called periodic of period p if there is an orientation preserving action of Z/p on S which preserves K setwise and its fixed point set A is a circle disjoint to K. A is called the axis. Two periodic knots K0 and K1 of period p are called equivariantly concordant...
متن کاملOn Equivariant Slice Knots
We suggest a method to detect that two periodic knots are not equivariantly concordant, using surgery on factor links. We construct examples which satisfy all known necessary conditions for equivariant slice knots— Naik’s and Choi-Ko-Song’s improvements of classical results on Seifert forms and Casson-Gordon invariants of slice knots — but are not equivariantly slice.
متن کاملFiltrations of Global Equivariant K-theory
In [AL07] and [AL10], Arone and Lesh constructed and studied spectrum level filtrations that interpolate between connective (topological or algebraic) K-theory and the Eilenberg-MacLane spectrum for the integers. In this paper we consider (global) equivariant generalizations of these filtrations and of another closely related class of filtrations, the modified rank filtrations of the K-theory s...
متن کاملRing structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کامل