منابع مشابه
Immersions of Surfaces into Aspherical 3-manifolds
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 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}...
متن کاملImmersions of Non-orientable Surfaces
Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R, with values in any Abelian group. We show they are all functions of the universal order 1 invariant that we construct as T ⊕ P ⊕Q where T is a Z valued invariant reflecting the number of triple points of the immersion, and P,Q are Z/2 valued invariants characterized by the property that ...
متن کاملImmersions of Surfaces with Boundary into the Plane
Let f : M→R2 be a smooth immersion of a compact connected oriented surface with boundary M into R. Kauffman defined an equivalence relation called image homotopy and classified the set of all orientation preserving immersions of M into R up to image homotopy. When M is of genus one and the number of boundary components is strictly greater than one, Kauffman’s result requires a correction. In th...
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ژورنال
عنوان ژورنال: Topology
سال: 1986
ISSN: 0040-9383
DOI: 10.1016/0040-9383(86)90021-2