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- W2554938913 abstract "Bordism theory is a central object in algebraic topology.By now quite a few bordism invariants are known, e.g., Adams e-invariant for (stably) framed bordism, rho-invariants for equivariant bordism and Kreck-Stolz invariants for some versions of Spin^c-bordism.Bunke recently gave a unified construction for the mentioned bordism invariants, namely he defined the universal eta-invariant. This invariant is only defined on torsion elements in the particular bordism group. On the other hand some of the above invariants, e.g., some rho-invariants, are also defined on non-torsion elements.In this article we provide a non-canonical extension of the universal eta-invariant to non-torsion elements which we call intrinsic eta-invariant.To this end we introduce a new tool called universal geometrization.A universal geometrization is some data on a space B which generalizes the notion of universal connection in the case that B=BG is the classifying space of a compact Lie group.The technical heart of this article is to show that such universal geometrization exists in many situations.Moreover, we also classify these universal geometrizations and compute the intrinsic eta-invariant in examples.In the last part of the article we give a topological computation of the t-invariant due to Crowley and Goette which relies on the universal eta-invariant. Since our calculation is purely topological it serves as check of the previous ones due to Crowley and Goette." @default.
- W2554938913 created "2016-11-30" @default.
- W2554938913 creator A5014798567 @default.
- W2554938913 date "2015-06-01" @default.
- W2554938913 modified "2023-09-24" @default.
- W2554938913 title "Universal geometrizations and the intrinsic eta-invariant" @default.
- W2554938913 hasPublicationYear "2015" @default.
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