Formulae for order one invariants of immersions of surfaces

Tahl Nowik

doi:10.1016/j.aim.2005.09.003

Formulae for order one invariants of immersions of surfaces

Tahl Nowik

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The universal order 1 invariant f^U of immersions of a closed orientable surface into R³, whose existence has been established in [T. Nowik, Order one invariants of immersions of surfaces into 3-space, Math. Ann. 328 (2004) 261-283], is the direct sumf^U = under(⊕, n ∈ Z) f_n^H ⊕ under(⊕, n ∈ Z) f_n^T ⊕ M ⊕ Q where each f_n^H, f_n^T is a Z valued invariant and M, Q are Z / 2 valued invariants. An explicit formula for the value of Q on any embedding has been given in [T. Nowik, Automorphisms and embeddings of surfaces and quadruple points of regular homotopies, J. Differential Geom. 58 (2001) 421-455]. In the present work we give explicit formulae for the value of each f_n^H, f_n^T on all immersions, and for the value of M on any embedding.

Original language	English
Pages (from-to)	358-372
Number of pages	15
Journal	Advances in Mathematics
Volume	206
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2005.09.003
State	Published - 10 Nov 2006

Bibliographical note

Funding Information:
E-mail address: tahl@math.biu.ac.il. URL: http://www.math.biu.ac.il/~tahl. 1 Partially supported by the Minerva Foundation.

Keywords

Finite order invariants
Immersions of surfaces

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10.1016/j.aim.2005.09.003

Cite this

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title = "Formulae for order one invariants of immersions of surfaces",

abstract = "The universal order 1 invariant fU of immersions of a closed orientable surface into R3, whose existence has been established in [T. Nowik, Order one invariants of immersions of surfaces into 3-space, Math. Ann. 328 (2004) 261-283], is the direct sumfU = under(⊕, n ∈ Z) fnH ⊕ under(⊕, n ∈ Z) fnT ⊕ M ⊕ Q where each fnH, fnT is a Z valued invariant and M, Q are Z / 2 valued invariants. An explicit formula for the value of Q on any embedding has been given in [T. Nowik, Automorphisms and embeddings of surfaces and quadruple points of regular homotopies, J. Differential Geom. 58 (2001) 421-455]. In the present work we give explicit formulae for the value of each fnH, fnT on all immersions, and for the value of M on any embedding.",

keywords = "Finite order invariants, Immersions of surfaces",

author = "Tahl Nowik",

note = "Funding Information: E-mail address: tahl@math.biu.ac.il. URL: http://www.math.biu.ac.il/~tahl. 1 Partially supported by the Minerva Foundation.",

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doi = "10.1016/j.aim.2005.09.003",

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N2 - The universal order 1 invariant fU of immersions of a closed orientable surface into R3, whose existence has been established in [T. Nowik, Order one invariants of immersions of surfaces into 3-space, Math. Ann. 328 (2004) 261-283], is the direct sumfU = under(⊕, n ∈ Z) fnH ⊕ under(⊕, n ∈ Z) fnT ⊕ M ⊕ Q where each fnH, fnT is a Z valued invariant and M, Q are Z / 2 valued invariants. An explicit formula for the value of Q on any embedding has been given in [T. Nowik, Automorphisms and embeddings of surfaces and quadruple points of regular homotopies, J. Differential Geom. 58 (2001) 421-455]. In the present work we give explicit formulae for the value of each fnH, fnT on all immersions, and for the value of M on any embedding.

AB - The universal order 1 invariant fU of immersions of a closed orientable surface into R3, whose existence has been established in [T. Nowik, Order one invariants of immersions of surfaces into 3-space, Math. Ann. 328 (2004) 261-283], is the direct sumfU = under(⊕, n ∈ Z) fnH ⊕ under(⊕, n ∈ Z) fnT ⊕ M ⊕ Q where each fnH, fnT is a Z valued invariant and M, Q are Z / 2 valued invariants. An explicit formula for the value of Q on any embedding has been given in [T. Nowik, Automorphisms and embeddings of surfaces and quadruple points of regular homotopies, J. Differential Geom. 58 (2001) 421-455]. In the present work we give explicit formulae for the value of each fnH, fnT on all immersions, and for the value of M on any embedding.

KW - Finite order invariants

KW - Immersions of surfaces

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Formulae for order one invariants of immersions of surfaces

Abstract

Bibliographical note

Keywords

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