Tahl Nowik

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We classify all order one invariants of immersions of a closed orientable surface F into R 3 , 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 3 , the group of all order one invariants on A is isomorphic to G ℵ 0 ⊕ B ⊕ B where G ℵ 0 is the group of all functions from a set(More)
The universal order 1 invariant f U of immersions of a closed orientable surface into R 3 , 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 f U = n∈Z f H n ⊕ n∈Z f T n ⊕ M ⊕ Q where each f H n , f T n is a Z valued invariant and M, Q are Z/2(More)
We study random knots and links in R 3 using the Petaluma model, which is based on the petal projections developed in [2]. In this model we obtain a formula for the distribution of the linking number of a random two-component link. We also obtain formulas for the expectations and the higher moments of the Casson invariant and the order-3 knot invariant v3.(More)
Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R 3 , 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(More)
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T he theories as developed by European mathematicians prior to 1870 differed from the modern ones in that none of them used the modern theory of limits. Fermat develops what is sometimes called a " precalculus " theory, where the optimal value is determined by some special condition such as equality of roots of some equation. The same can be said for his(More)