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arXiv · 1511.06738

Splitting Madsen-Tillmann spectra II. The Steinberg idempotents and Whitehead conjecture

Takuji Kashiwabara·Hadi Zare
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Abstract

We show that, at the prime $p=2$, the spectrum $Σ^{-n}D(n)$ splits off the Madsen-Tillmann spectrum $MTO(n)=BO(n)^{-γ_n}$ which is compatible with the classic splitting of $M(n)$ off $BO(n)_+$. For $n=2$, together with our previous splitting result on Madsen-Tillmann spectra, this shows that $MTO(2)$ is homotopy equivalent to $BSO(3)_+\veeΣ^{-2}D(2)$.

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Takuji Kashiwabara, Hadi Zare. 2015-11-27. Splitting Madsen-Tillmann spectra II. The Steinberg idempotents and Whitehead conjecture. https://doi.org/10.2140/agt.2023.23.1935

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