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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:   To Appear
  Journal: Algebraic and Geometric Topology
  Supported by:  IPM
  Abstract:
We show that, at the prime p=2, the spectrum ΣnD(n) splits off the Madsen-Tillmann spectrum MTO(n)=BO(n)−γn 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)+∨Σ−2D(2).

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