The nonorientable 4-genus of knots

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August undefined, 2024

WebGiven a knot in the 3-sphere, the non-orientable 4-genus or 4-dimensional crosscap number of a knot is the minimal first Betti number of non-orientable surfaces, smoothly and … WebMay 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 …

[1005.5473] The nonorientable four-genus of knots - arXiv.org

WebNov 18, 2014 · Unoriented Knot Floer Homology and the Unoriented Four-Ball Genus August 2015 · In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying the... http://export.arxiv.org/abs/2011.03480 breadbox\\u0027s w6

@F F arXiv:2007.14332v1 [math.GT] 28 Jul 2024

WebWe develop obstructions to a knot K⊂S3 bounding a smooth punctured Klein bottle in B4. The simplest of these is based on the linking form of the 2-fold branched cover of S3 … WebThenonorientable4-genus (K) is the minimum rst Betti number of nonorientable surfaces inB4bounded byK. For a slice knot, it is de ned to be 0 instead of 1. Shibuya [16] de ned the 4-dimensional clasp number c(K) to be the minimum number of the double points of transversely immersed 2-disks inB4bounded byK. Shibuya [16] gave the following inequality WebSep 22, 2024 · components and its number of \holes," which we call the genus of the surface (the plural of genus is genera). For a proof of Theorem 2, see [4]. 4 Seifert surfaces A Seifert surface for a knot K is a compact, orientable, connected surface with boundary equal to K. By the previous section, any such surface must be topologically 3 cory\u0027s famous mac and cheese

On the periodic non-orientable 4-genus of a knot Request PDF

WebWe develop obstructions to a knot K⊂S3 bounding a smooth punctured Klein bottle in B4. The simplest of these is based on the linking form of the 2-fol We use cookies to enhance … WebNov 6, 2024 · Abstract: Given a knot in the 3-sphere, the non-orientable 4-genus or 4-dimensional crosscap number of a knot is the minimal first Betti number of non-orientable … breadbox\\u0027s w9WebNov 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 breadbox\\u0027s wb

"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 … " - The nonorientable 4-genus of knots

The nonorientable 4-genus of knots

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.

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WebNov 6, 2024 · Abstract:Given a knot in the 3-sphere, the non-orientable 4-genus or 4-dimensional crosscap number of a knot is the minimal first Betti number of non-orientable … Webitself (i.e. crossing changes) to obtain the unknot (i.e. a knot which bounds a disk). The genus of a knot K is g(K) = minfg() : ˆS. 3;@ = K; is an orientable surface gwhere g() denotes the genus of a surface . Related invariants are the 4-ball genus and nonorientable 4-ball genus. Note that the boundary of B. 4. is equal to S. 3

WebWe develop obstructions to a knot K in the 3-sphere bounding a smooth punctured Klein bottle in the 4-ball. The simplest of these is based on the linking form of the 2-fold … WebNov 6, 2024 · The nonorientable 4-genus of knots, J. Lond. Math. Soc. (2) 84 ( 3) ( 2011 ), 559 – 577. CrossRef Google Scholar 8 Gordon, C. McA., Litherland, R. A. and Murasugi, K., …

WebThe 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. 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 …

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.

WebSep 5, 2024 · The non-orientable 4-genus of a knot in the 3-sphere is defined as the smallest first Betti number of any non-orientable surface smoothly and properly embedded in the 4-ball, with boundary the ... breadbox\\u0027s wcWebOct 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... breadbox\u0027s wcWebnonorientable 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 … cory\u0027s first video