Geodesic
Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space
Fundamenta Mathematicae, Tome 162 (1999) no. 3, pp. 209-232.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated in even degrees.
DOI : 10.4064/fm-162-3-209-232

Marta Santos 1

1 
@article{10_4064_fm_162_3_209_232,
     author = {Marta Santos},
     title = {Brown{\textendash}Peterson cohomology and {Morava} {K-theory} of {DI(4)} and its classifying space},
     journal = {Fundamenta Mathematicae},
     pages = {209--232},
     publisher = {mathdoc},
     volume = {162},
     number = {3},
     year = {1999},
     doi = {10.4064/fm-162-3-209-232},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-162-3-209-232/}
}
TY  - JOUR
AU  - Marta Santos
TI  - Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space
JO  - Fundamenta Mathematicae
PY  - 1999
SP  - 209
EP  - 232
VL  - 162
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-162-3-209-232/
DO  - 10.4064/fm-162-3-209-232
LA  - en
ID  - 10_4064_fm_162_3_209_232
ER  - 
%0 Journal Article
%A Marta Santos
%T Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space
%J Fundamenta Mathematicae
%D 1999
%P 209-232
%V 162
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-162-3-209-232/
%R 10.4064/fm-162-3-209-232
%G en
%F 10_4064_fm_162_3_209_232
Marta Santos. Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space. Fundamenta Mathematicae, Tome 162 (1999) no. 3, pp. 209-232. doi : 10.4064/fm-162-3-209-232. http://geodesic.mathdoc.fr/articles/10.4064/fm-162-3-209-232/

Cité par Sources :