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Order one invariants of immersions of surfaces into 3-space

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Abstract

We classify all order one invariants of immersions of a closed orientable surface F into ℝ3, with values in an arbitrary Abelian group . We show that for any F and and any regular homotopy class of immersions of F into ℝ3, the group of all order one invariants on is isomorphic to is the group of all functions from a set of cardinality . Our work includes foundations for the study of finite order invariants of immersions of a closed orientable surface into ℝ3, analogous to chord diagrams and the 1-term and 4-term relations of knot theory.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Tahl Nowik

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  1. Tahl Nowik
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Correspondence to Tahl Nowik.

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Partially supported by the Minerva Foundation

Mathamatics Subject Classification (2000): 57M, 57R42

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Nowik, T. Order one invariants of immersions of surfaces into 3-space. Math. Ann. 328, 261–283 (2004). https://doi.org/10.1007/s00208-003-0482-1

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  • DOI: https://doi.org/10.1007/s00208-003-0482-1

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