The nonorientable 4-genus of knots
WebWe show that the equivariant and non-equivariant non-orientable 4-genus of p-periodic knots may differ, for any choice of p ≥ 2.Similar results have previously been obtained for the smooth 4-genus and non-orientable 3-genus of a periodic knot. WebBatson's conjecture is a nonorientable version of Milnor's conjecture which states that the nonorientable 4-ball genus is equal to the pinch number of a torus knot, i.e. the number of a specific type of (nonorientable) band surgeries needed to obtain the unknot. The conjecture was recently proved to be false by Lobb.
The nonorientable 4-genus of knots
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Webgenus and adds infinitely many copies of this curve (in the sense of addition of knots), but scales them down successively in length so that the final curve has finite length. Corollary 3. Any rectifiable Jordan curve of infinite genus bounds infinitely many ( orientable and nonorientable} minimal surfaces. WebMay 1, 2015 · In [7], we defined the non-orientable genera of knots in punc X as follows. Definition Let X be a closed 4-manifold and K ⊂ ∂ ( punc X) ( ≅ S 3) a knot. The non …
WebGiven a nonorientable surface with boundary a knot, an analysis of the existing methods for bounding and computing the nonorientable 4-genus reveals relationships between the first Betti number and the normal Euler class of the surface. WebSep 19, 2024 · The nonorientable four-ball genus of a knot in is the minimal first Betti number of nonorientable surfaces in bounded by . By amalgamating ideas from involutive knot Floer homology and unoriented knot Floer homology, we give a new lower bound on the smooth nonorientable four-ball genus of any knot.
WebNov 6, 2024 · the non-orient able 4-genus for knots with 10 crossings 11 (a) If φ ( e 3 ) = − f 3 + f 5 + f 6 then φ ( e 2 ) = − f 5 + f 1 − f 2 . Let φ ( e 1 ) = P 6 WebWe develop obstructions to a knot bounding a smooth punctured Klein bottle in . The simplest of these is based on the linking form of the 2–fold branched cover of branched over . Stronger obstructions are based on th…
WebNov 6, 2024 · The non-orientable 4-genus for knots with 10 crossings. Given a knot in the 3-sphere, the non-orientable 4-genus or 4-dimensional crosscap number of a knot is the …
Webstudy the relation between the 4-genus (slice genus) and the 4-dimensional clasp number. We also introduce another four-dimensional numerical invariant, the nonorientable 4-genus, for knots. The 4-genus g* (K) of a knot K in S3 = &B4 is the minimum genus of orientable surfaces in B4 bounded by K [5]. The nonorientable 4-genus $* (K) is the minimum phillip island 7 day weatherWebMay 29, 2010 · The nonorientable 4-genus of knots Authors: Patrick M. Gilmer Louisiana State University Charles Livingston Abstract We develop obstructions to a knot K in the 3 … tryout resultsWebThe non-orientablegenus, demigenus, or Euler genusof a connected, non-orientable closed surface is a positive integer representing the number of cross-capsattached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k, where kis the non-orientable genus. phillip island activities for kidsWebnonorientable 4-genus of all prime knots up through 10 crossings [11, 16]. (Note that [11, 16], as well as KnotInfo [22], de ne 4 of a slice knot to be one rather than the original de nition of zero. Furthermore, the invariant is called … tryout requirements for volleyballWebOct 4, 2024 · We show that the equivariant and non-equivariant non-orientable 4-genus of [Formula: see text]-periodic knots may differ, for any choice of [Formula: see text]. Similar results have previously... try out sbmptn gratisWebFeb 25, 2024 · 2. In the book "Topology Now!" by Robert Messer one of the practice problem suggests, " One could define the nonorientable genus of a knot to be zero for the trivial knot, and for any other knot K to be the smallest number p such that the surface formed by taking; the connected sum of p projective plans and removing one disk will span K ". tryouts bring it on lyricsWebAug 19, 2011 · We develop obstructions to a knot K⊂S 3 bounding a smooth punctured Klein bottle in B 4.The simplest of these is based on the linking form of the 2-fold branched … try out sbmptn soshum gratis