An obstruction to knots bounding Mobius bands in B4
by Kearney, Mary Katherine, Ph.D., INDIANA UNIVERSITY, 2011, 57 pages; 3488339

Abstract:

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 thesis focuses on a particular case of this question, namely whether a given knot in the three-sphere can be the boundary of a Möbius band embedded in the four-ball, B4. We introduce a new obstruction to a knot bounding a Möbius band in B 4, using the d-invariant of Heegaard-Floer theory. We also explore applications of this obstruction to several examples. In particular, we give a new example of a knot which does not bound a Möbius band in B4.
 
AdviserCharles Livingston
SchoolINDIANA UNIVERSITY
SourceDAI/B 73-04, p. , Jan 2012
Source TypeDissertation
SubjectsMathematics
Publication Number3488339
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