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- Joel Hass, Tahl Nowik
- 2008

We construct a new order 1 invariant for knot diagrams. We use it to determine the minimal number of Reidemeister moves needed to pass between certain pairs of knot diagrams.

- Joel Hass, Tahl Nowik
- Discrete & Computational Geometry
- 2010

We present a sequence of diagrams of the unknot for which the minimum number of Reidemeister moves required to pass to the trivial diagram is quadratic with respect to the number of crossings. These bounds apply both in S 2 and in R 2 .

- Tahl Nowik, T. Nowik
- 2003

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)

- TAHL NOWIK
- 1998

Let GI denote the space of all generic immersions of a surface F into a 3-manifold M. Let q(H R) denote the number mod 2 of quadruple points of a generic regular homotopy H R : FPM. We are interested in de"ning an invariant Q : GIP9/2 such that q(H R)"Q(H)!Q(H) for any generic regular homotopy H R : FPM. Such an invariant exists i! q"0 for any closed… (More)

- TAHL NOWIK
- 2006

We classify all finite order invariants of immersions of a closed orientable surface into R 3 , with values in any Abelian group. We show that they are all functions of order one invariants.

- TAHL NOWIK
- 2002

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)

- Chuichiro Hayashi, Miwa Hayashi, Tahl Nowik
- 2012

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a r t i c l e i n f o a b s t r a c t MSC: 57M25 Keywords: Link diagram Reidemeister… (More)

- TAHL NOWIK
- 2008

We show that the maximal number of singular moves required to pass between any two regularly homotopic planar or spherical curves with at most n crossings, grows quadratically with respect to n. Furthermore, this can be done with all curves along the way having at most n + 2 crossings.

- Chaim Even-Zohar, Joel Hass, Nathan Linial, Tahl Nowik
- Discrete & Computational Geometry
- 2016

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)

- Tahl Nowik
- 2005

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)