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Bulletin of the London Mathematical Society Advance Access originally published online on December 14, 2006
Bulletin of the London Mathematical Society 2007 39(1):39-45; doi:10.1112/blms/bdl009
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© 2006 London Mathematical Society

An Ekholm–Szucs-type formula for codimension one immersions of 3-manifolds up to bordism

Masamichi Takase

Department of Mathematics
University of Iowa
14 MacLean Hall
Iowa City, IA 52242-1419
USA
mtakase{at}math.uiowa.edu

Received 14 August 2005. Revision received 10 January 2006.

We give a formula for the bordism class of an immersion of an oriented 3-manifold in 4-space. It expresses the class in terms of the topology of a null-cobordism of the 3-manifold and certain singularities (the number of umbilic points) of a generic map of this null-cobordism into 4-space which extends the immersion.

Current address: Department of Mathematical Sciences Faculty of Science Shinsu University Matsumoto 390–8621 Japan takase{at}math.shinsu-u.ac.jp


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