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Item Details
| Title:
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V1-PERIODIC HOMOTOPY GROUPS OF SO(N)
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| By: |
Martin Bendersky, Donald Davis |
| Format: |
Paperback |
| List price:
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£61.95 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821835890 |
| ISBN 13: |
9780821835890 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 September, 2004 |
| Series: |
Memoirs of the American Mathematical Society No. 172 |
| Pages: |
90 |
| Description: |
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 $\operatorname{Spin}(n)$. |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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