v[1]-periodic homotopy groups of SO(n)
著者
書誌事項
v[1]-periodic homotopy groups of SO(n)
（Memoirs of the American Mathematical Society, no. 815）
American Mathematical Society, 2004
大学図書館所蔵 件 / 全14件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
"November 2004, Volume 172, number 815 (end of volume)"
Bibliography: p. 89-90
On t.p. "[1]" is subscript
内容説明・目次
内容説明
We compute the 2-primary $v_1$-periodic homotopy groups of the special orthogonal groups $SO(n)$. The method is to calculate the Bendersky-Thompson spectral sequence, a $K_*$-based unstable homotopy spectral sequence, of $\operatorname{Spin}(n)$. The $E_2$-term is an Ext group in a category of Adams modules. Most of the differentials in the spectral sequence are determined by naturality from those in the spheres. The resulting groups consist of two main parts. One is summands whose order depends on the minimal exponent of 2 in several sums of binomial coefficients times powers. The other is a sum of roughly $[\log_2(2n/3)]$ copies of ${\bold Z}/2$. As the spectral sequence converges to the $v_1$-periodic homotopy groups of the $K$-completion of a space, one important part of the proof is that the natural map from $\operatorname{Spin}(n)$ to its $K$-completion induces an isomorphism in $v_1$-periodic homotopy groups.
目次
Introduction The BTSS of ${\rm BSpin}(n)$ and the CTP Listing of results The 1-line of ${\rm Spin}(2n)$ Eta towers $d_3$ on eta towers Fine tuning Combinatorics Comparison with $J$-homology approach Proof of fibration theorem A small resolution for computing ${\rm ext}_{\mathcal A}$ Bibliography.
「Nielsen BookData」 より