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Mar 27 at 18:13 comment added Ian Agol The quotient of a 3-manifold by a circle action will be an orbifold. If there are no fixed points of the action, then the quotient is a closed orbifold. These are known to be null-cobordant. msp.org/pjm/2000/193-1/p04.xhtml One could then try to extend the circle action to an action over the 3-manifold bounding the orbifold (but I haven’t tried to do this myself).
Mar 17 at 6:04 comment added Ryan Budney I don't work in $S^1$-equivariant bordism but there has been some considerable work in this area. Here is a recent paper on the topic. arxiv.org/pdf/1506.04073.pdf
Mar 17 at 4:26 history asked Zhiqiang CC BY-SA 4.0