An Obstruction to Knots Bounding Mobius Bands in B^4

The relationship between embedded surfaces and their knotted boundaries has been one of the main topics of knot theory for much of the last half century. This talk focuses on a particular case, namely whether a given knot in the three-sphere can be the boundary of a Mobius band embedded in the four-ball, B^4. We will discuss a new example of a knot which does not bound a Mobius band in B^4, and describe how the d-invariant of Heegaard-Floer theory is used to obstruct this and other knots from bounding Mobius bands in B^4.