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Let F be a closed surface. If i, i : F → R 3 are two regularly homotopic generic immersions, then it has been shown in [5] that all generic regular homotopies between i and i have the same number mod 2 of quadruple points. We denote this number by Q(i, i) ∈ Z/2. For F orientable we show that for any generic immersion i : F → R 3 and any diffeomorphism h : F(More)
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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)
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)