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

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 $BSO(3)_+\vee\Sigma^{-2}D(2)$.Comment: Comments are welcome

Carlton M. Bo Reid

Former MSU football player Carlton M. Bo Reid is pictured wearing a football uniform as he appears to be running.https://scholarsjunction.msstate.edu/ua-photo-collection/5371/thumbnail.jp

Is there a relationship between prism fusion range and vergence facility?

Aim: To investigate the relationship between prism fusion range (PFR) and vergence facility (VF) measurements in subjects with normal binocular vision. Methods: Twenty-eight subjects (mean age 19 ± 1 years) with normal binocular single vision (BSV) underwent measurement of the PFR and VF in a varied order, at a test distance of 1/3 m. The PFR measurements recorded were the base out (BO) range to blur and break point and base in (BI) range to break point. The total PFR was calculated. The VF was assessed over a 1 min time period using a 12(Δ)BO/ 3(Δ)BI flip prism and recorded in cycles per minute (cpm). Results: No correlation was demonstrable between any of the single measures of the PFR and the VF results. The BO PFR to break point and the BI PFR results obtained (means 46(Δ) BO and 14(Δ) BI) were not significantly different from quoted ‘normal’ values. The VF results obtained (mean 12 ± 4.2 cpm) were found to be significantly different from the reported mean value. Conclusion: In a group of young adults with normal BSV, no correlation between PFR and VF was found. The two tests may quantify different aspects of vergence or, alternatively, results of one or both tests in this study may be unreliable