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