Geodesic
A May-type spectral sequence for higher topological Hochschild homology
Angelini-Knoll, Gabe1 ; Salch, Andrew2
1 Department of Mathematics, Michigan State University, East Lansing, MI, United States
2 Department of Mathematics, Wayne State University, Detroit, MI, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2593-2660

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Given a filtration of a commutative monoid A in a symmetric monoidal stable model category C, we construct a spectral sequence analogous to the May spectral sequence whose input is the higher order topological Hochschild homology of the associated graded commutative monoid of A, and whose output is the higher order topological Hochschild homology of A. We then construct examples of such filtrations and derive some consequences: for example, given a connective commutative graded ring R, we get an upper bound on the size of the THH–groups of E∞ –ring spectra A such that π∗(A)≅R.

DOI : 10.2140/agt.2018.18.2593
Classification : 18G30, 19D55, 55P42, 55T05
Keywords: homotopy theory, higher topological Hochschild homology, spectral sequences, filtered commutative monoid, Whitehead tower

Angelini-Knoll, Gabe 1 ; Salch, Andrew 2

1 Department of Mathematics, Michigan State University, East Lansing, MI, United States
2 Department of Mathematics, Wayne State University, Detroit, MI, United States 
@article{10_2140_agt_2018_18_2593,
     author = {Angelini-Knoll, Gabe and Salch, Andrew},
     title = {A {May-type} spectral sequence for higher topological {Hochschild} homology},
     journal = {Algebraic and Geometric Topology},
     pages = {2593--2660},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {2018},
     doi = {10.2140/agt.2018.18.2593},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2593/}
}
TY  - JOUR
AU  - Angelini-Knoll, Gabe
AU  - Salch, Andrew
TI  - A May-type spectral sequence for higher topological Hochschild homology
JO  - Algebraic and Geometric Topology
PY  - 2018
SP  - 2593
EP  - 2660
VL  - 18
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2593/
DO  - 10.2140/agt.2018.18.2593
ID  - 10_2140_agt_2018_18_2593
ER  - 
%0 Journal Article
%A Angelini-Knoll, Gabe
%A Salch, Andrew
%T A May-type spectral sequence for higher topological Hochschild homology
%J Algebraic and Geometric Topology
%D 2018
%P 2593-2660
%V 18
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2593/
%R 10.2140/agt.2018.18.2593
%F 10_2140_agt_2018_18_2593
Angelini-Knoll, Gabe; Salch, Andrew. A May-type spectral sequence for higher topological Hochschild homology. Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2593-2660. doi: 10.2140/agt.2018.18.2593

Cité par Sources :