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Paper   IPM / M / 16956
School of Mathematics
  Title:   Splitting Madsen-Tillmann spectra II. The Steinberg idempotents and Whitehead conjecture
  Author(s):  Hadi Zare (Joint with T. Kashiwabara)
  Status:   Published
  Journal: Algebraic and Geometric Topology
  Vol.:  23
  Year:  2023
  Pages:   1935-1957
  Supported by:  IPM
  Abstract:
We show that, at the prime $p=2$, the spectrum $\Sigma^{-n}D(n)$ splits off the Madsen-Tillmann spectrum $MTO(n)=BO(n)^{-\gamma_n}$ 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 $BSO(3)_+\vee\Sigma^{-2}D(2)$.

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