Journal of the Ramanujan Mathematical Society

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Non-Orientable Seifert Surfaces and A Thom-Pontrjagin Type Construction


Affiliations
1 Department of Mathematics, Indian Institute of Science, Bangalore 560 003, India
2 School of Mathematics, Tata Institute of Fundamental Research, Mumbai 400 005, India
     

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We give a new proof of a theorem of Gordon and Litherland that two non-orientable Seifert surfaces for a framed knot are isotopic after finitely many stabilisations. This is based on a non-orientable version of a relative Thom-Pontrjagin construction using as a model a triple of spaces consisting of the solid Klein bottle, the Klein bottle and an orientation reversing curve on the Klein bottle. Our construction applies to all smooth codimension two knots in spheres.
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  • Non-Orientable Seifert Surfaces and A Thom-Pontrjagin Type Construction

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Authors

Siddhartha Gadgil
Department of Mathematics, Indian Institute of Science, Bangalore 560 003, India
Dishant Pancholi
School of Mathematics, Tata Institute of Fundamental Research, Mumbai 400 005, India

Abstract


We give a new proof of a theorem of Gordon and Litherland that two non-orientable Seifert surfaces for a framed knot are isotopic after finitely many stabilisations. This is based on a non-orientable version of a relative Thom-Pontrjagin construction using as a model a triple of spaces consisting of the solid Klein bottle, the Klein bottle and an orientation reversing curve on the Klein bottle. Our construction applies to all smooth codimension two knots in spheres.