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We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups.
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This content will become publicly available on September 1, 2026
New examples of topologically slice links
In 2007, Cochran–Friedl–Teichner gave sufficient conditions for when a link obtained by multi-infection is topologically slice involving a Milnor’s invariant condition on the infecting string link. In this paper, we give a different Milnor’s invariant condition which can handle some cases which the original theorem cannot. Along the way, we also give sufficient conditions for a multi-infection to be [Formula: see text]-solvable, where we require that the infecting string link have vanishing pairwise linking numbers, which can be seen as handling an additional “[Formula: see text]-solvable” case of a well-known result about the relationship between satellite operations and the solvable filtration of Cochran–Orr–Teichner.
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- PAR ID:
- 10647321
- Publisher / Repository:
- World Scientific
- Date Published:
- Journal Name:
- Journal of Knot Theory and Its Ramifications
- Volume:
- 34
- Issue:
- 10
- ISSN:
- 0218-2165
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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