## The generalized Tate construction

##### Author(s)

Stroilova, Olga (Olga Y.)
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Haynes R. Miller.

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Show full item record##### Abstract

The purpose of this work is give some field notes on exploring the idea that a generalized Tate construction tk reduces chromatic level in stable homotopy theory. The first parts introduce the construction and discuss chromatic reduction. The next section makes a computation and gives the duals of L(n) = L(n)1. The last part looks ahead, mentioning how this computation could be extended to finding the duals of Steinberg summands in corresponding Thom spectra of negative representations, L(n)-q, and presents an equivariant loopspace machine. Finally, observations made are pulled together and brought back to compute the base case of the generalized Tate construction, evaluated on a sphere. Results parallel work of A. Cathcart, B. Guillou and P. May, and N. Stapleton, among others.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 69-70).

##### Date issued

2012##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.