V1-periodic Homotopy Groups of SO(n)

Martin Bendersky, Donald Davis (Autoren)

Buch | Softcover

2005
American Mathematical Society (Verlag)
978-0-8218-3589-0 (ISBN)

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Computes 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 $/operatorname{Spin}(n)$.

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.

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.

Erscheint lt. Verlag	1.1.2005
Reihe/Serie	Memoirs of the American Mathematical Society
Zusatzinfo	illustrations
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-3589-0 / 0821835890
ISBN-13	978-0-8218-3589-0 / 9780821835890
Zustand	Neuware