Formulae for order one invariants of immersions of surfaces
نویسنده
چکیده
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 sum
منابع مشابه
Order one invariants of immersions of surfaces into 3 - space
We classify all order one invariants of immersions of a closed orientable surface F into R3, with values in an arbitrary Abelian group G. We show that for any F and G and any regular homotopy class A of immersions of F into R3, the group of all order one invariants on A is isomorphic to Gא0 ⊕B⊕B where Gא0 is the group of all functions from a set of cardinality א0 into G and B = {x ∈ G : 2x = 0}...
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The universal order 1 invariant f of immersions of a closed orientable surface into R, whose existence has been established in [N3], takes values in the group GU = K⊕Z/2⊕Z/2 where K is a countably generated free Abelian group. The projections of f to K and to the first and second Z/2 factors are denoted f , M, Q respectively. An explicit formula for the value of Q on any embedding has been give...
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We study finite order invariants of null-homotopic immersions of a closed orientable surface into an aspherical orientable 3-manifold. We give the foundational constructions, and classify all order one invariants.
متن کاملHigher Order Invariants of Immersions of Surfaces into 3-space
Finite order invariants of stable immersions of a closed orientable surface into R have been defined in [N], where all order 1 invariants have been classified. In the present work we classify all finite order invariants of order n > 1, and show that they are all functions of the universal order 1 invariant constructed in [N]. The structure of the paper is as follows: In Section 2 we summarize t...
متن کاملOrder One Invariants of Immersions
We classify all order one invariants of immersions of a closed orientable surface F into R, with values in an arbitrary Abelian group G. We show that for any F and G and any regular homotopy class A of immersions of F into R, the group of all order one invariants on A is isomorphic to G0 ⊕ B ⊕ B where G0 is the group of all functions from a set of cardinality א0 into G and B = {x ∈ G : 2x = 0}....
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تاریخ انتشار 2005