## V1-periodic Homotopy Groups of SO(n)

Author: Martin Bendersky,Donald M. Davis

Publisher: American Mathematical Soc.

ISBN: 0821835890

Category: Mathematics

Page: 90

View: 8275

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.
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## V1-periodic Homotopy Groups of SO(n)

Author: Martin Bendersky,Donald M. Davis

Publisher: American Mathematical Soc.

ISBN: 0821835890

Category: Mathematics

Page: 90

View: 7240

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.
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## Topology and Representation Theory

Conference on the Connections Between Topology and Representation Theory, May 1-5, 1992, Northwestern University

Author: Eric M. Friedlander,Mark E. Mahowald,American Mathematical Society

Publisher: American Mathematical Soc.

ISBN: 0821851659

Category: Mathematics

Page: 318

View: 6889

During 1991-1992, Northwestern University conducted a special emphasis year on the topic, 'The connections between topology and representation theory'. Activities over the year culminated in a conference in May 1992 which attracted over 120 participants. Most of the plenary lectures at the conference were expository and designed to introduce current trends to graduate students and nonspecialists familiar with algebraic topology. This volume contains refereed papers presented or solicited at the conference; one paper is based on a seminar given during the emphasis year.
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## Books in Print Supplement

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 513

Includes authors, titles, subjects.
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## Arrugas en el tiempo

Author: George Smoot,Keay Davidson

Publisher: Grano de Sal

ISBN: 6079824922

Category: Science

Page: 328

View: 9944