Project description

The purpose of this project is a better understanding of the irreducible components of the Thom spectra $MSU$ and $MU\langle 6\rangle$ associated to connected covers of $BU$. At $p=2$ Pengelley constructed a spectrum $BoP$ which sits inside $MSU$ as an irreducible direct summand. It comes with a ring map to $ko$ which on homotopy groups is onto in all degrees and injective in odd degrees. We like to give a new construction of this spectrum and to show that a similar irreducible component appears in $MU\langle 6\rangle$. This would be a suitably defined amalgam of $tmf$ with $BP$. The spectrum $MU\langle 6\rangle$ has come into the focus of current research because it is related to string theory in mathematical physics.

Related publications

Laures, G. and Olbermann, M..Cannibalistic classes of string bundles. Manuscripta Math. 156 (2018), no. 3-4, 273–298.

Laures, G. and Schuster, B.  Towards a splitting of the K(2)-local string bordism spectrum, Proc. Amer. Math. Soc. 147 (2019), no. 1, 399–410.

Gerd Laures, Characteristic classes in $TMF$ of level $\Gamma_1(3)$, Trans. Amer. Math. Soc. 368 (2016), no. 10, 7339--7357.

Gerd Laures and Martin Olbermann, $TMF_0(3)$-characteristic classes for string bundles, Math. Z. 282 (2016), no. 1-2, 511--533.

Nils Schulenberg, Indecomposable Summands in Real and Complex Thom Spectra (thesis 2019) docId/6555