Some properties of the Thom spectrum over loop suspension of complex projective space

Andrew Baker; Birgit Richter

Some properties of the Thom spectrum over loop suspension of complex projective space

Algebraic Topology 2013-01-18 v2

Authors: Andrew Baker , Birgit Richter

Abstract

This note provides a reference for some properties of the Thom spectrum $M\xi$ over $\Omega\Sigma\CPi$ . Some of this material is used in recent work of Kitchloo and Morava. We determine the $M\xi$ -cohomology of $\CPi$ and show that $M\xi^*(\CPi)$ injects into power series over the algebra of non-symmetric functions. We show that $M\xi$ gives rise to a commutative formal group law over the non-commutative ring $\pi_*M\xi$ . We also discuss how $M\xi$ and some real and quaternionic analogues behave with respect to spectra that are related to these Thom spectra by splittings and by maps.

Keywords

Thom spectrum loop suspension complex projective space cohomology formal group law non-symmetric functions spectra

Cite

@article{arxiv.1207.4947,
  title  = {Some properties of the Thom spectrum over loop suspension of complex projective space},
  author = {Andrew Baker and Birgit Richter},
  journal= {arXiv preprint arXiv:1207.4947},
  year   = {2013}
}

Comments

Final version - to appear in Contemporary Mathematics volume Proceedings of the Fourth Arolla Conference on Algebraic Topology. Various changes made improving details of exposition and proofs

Some properties of the Thom spectrum over loop suspension of complex projective space

Abstract

Keywords

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