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Sphere bundles with 1/4-pinched fiberwise metrics

Farrell, Thomas and Gang, Zhou and Knopf, Dan and Ontaneda, Pedro (2017) Sphere bundles with 1/4-pinched fiberwise metrics. Transactions of the American Mathematical Society, 369 (9). pp. 6613-6630. ISSN 0002-9947.

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We prove that all smooth sphere bundles that admit fiberwise 1/4-pinched metrics are induced bundles of vector bundles, so their structure groups reduce from DIFF(S^n) to O(n+1). This result implies the existence of many smooth S^n-bundles over S^k that do not support strictly 1/4-pinched positively curved Riemannian metrics on their fibers.

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Additional Information:© 2017 American Mathematical Society. Received by editor(s): April 21, 2016; Received by editor(s) in revised form: June 8, 2016; Published electronically: May 16, 2017. The first and fourth authors thank NSF for support in DMS-1206622. The second author thanks NSF for support in DMS-1308985 and DMS-1443225. The third author thanks NSF for support in DMS-1205270.
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Issue or Number:9
Classification Code:2010 Mathematics Subject Classification: Primary 57R22; Secondary 53C44
Record Number:CaltechAUTHORS:20170831-134035097
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81027
Deposited By: Tony Diaz
Deposited On:31 Aug 2017 20:55
Last Modified:03 Oct 2019 18:37

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