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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1304.4759 |
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| _version_ | 1866916668584755200 |
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| author | Laures, Gerd McClure, James E. |
| author_facet | Laures, Gerd McClure, James E. |
| contents | We give a simple sufficient condition for Quinn's "bordism-type" spectra to be weakly equivalent to commutative symmetric ring spectra. We also show that the symmetric signature is (up to weak equivalence) a monoidal transformation between symmetric monoidal functors, which implies that the Sullivan-Ranicki orientation of topological bundles is represented by a ring map between commutative symmetric ring spectra. In the course of proving these statements we give a new description of symmetric L theory which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_4759 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Commutativity properties of Quinn spectra Laures, Gerd McClure, James E. Algebraic Topology 55P43, 57R67, 57P10 We give a simple sufficient condition for Quinn's "bordism-type" spectra to be weakly equivalent to commutative symmetric ring spectra. We also show that the symmetric signature is (up to weak equivalence) a monoidal transformation between symmetric monoidal functors, which implies that the Sullivan-Ranicki orientation of topological bundles is represented by a ring map between commutative symmetric ring spectra. In the course of proving these statements we give a new description of symmetric L theory which may be of independent interest. |
| title | Commutativity properties of Quinn spectra |
| topic | Algebraic Topology 55P43, 57R67, 57P10 |
| url | https://arxiv.org/abs/1304.4759 |