Constructions of Lagrangian Cobordisms

Blackwell, Sarah E.; Legout, Noémie; Leverson, Caitlin; Limouzineau, Maÿlis; Myer, Ziva; Pan, Yu; Pezzimenti, Samantha; Suárez, Lara Simone; Traynor, Lisa

doi:10.1007/978-3-030-80979-9_5

Cited by 1 publication

(3 citation statements)

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“…As noted by Batson [3], we may use the normal Euler number to refine the minimal 4-dimensional crosscap number of a knot in S 3 . The e-crosscap number cr e (K) of a knot K is the minimal first Betti number of all properly embedded non-orientable surfaces F ⊂ B 4 with ∂F = K and e(F) = e. The 4-dimensional crosscap number cr 4 (K) is simply the minimum value of cr e (K).…”

Section: •1 the Normal Euler Numbermentioning

confidence: 99%

“…It is useful to introduce some notation: denote the decomposition of L into elementary cobordisms by L = L 1 • • • L n , with L i going from i−1 to i . For more information about constructing Lagrangian cobordisms, see [4].…”

Section: •2 Lagrangian Cobordismsmentioning

confidence: 99%

“…The motivating question for this paper is: given a Legendrian link ⊂ (S 3 , ξ 0 ), how does the existence of an exact Lagrangian filling L ⊂ (B 4 , ω 0 ), orientable or not, restrict the smooth knot type of ? We say that a smooth knot K is (orientably or non-orientably) Lagrangian fillable if it has a Legendrian representative that has an exact (orientable or non-orientable) Lagrangian filling.…”

Section: Introductionmentioning

confidence: 99%

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Non-Orientable Lagrangian Fillings of Legendrian Knots

CHEN,

CRIDER-PHILLIPS,

REINOSO

et al. 2023

Math. Proc. Camb. Phil. Soc.

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We investigate when a Legendrian knot in the standard contact ${{\mathbb{R}}}^3$ has a non-orientable exact Lagrangian filling. We prove analogs of several results in the orientable setting, develop new combinatorial obstructions to fillability, and determine when several families of knots have such fillings. In particular, we completely determine when an alternating knot (and more generally a plus-adequate knot) is decomposably non-orientably fillable and classify the fillability of most torus and 3-strand pretzel knots. We also describe rigidity phenomena of decomposable non-orientable fillings, including finiteness of the possible normal Euler numbers of fillings and the minimisation of crosscap numbers of fillings, obtaining results which contrast in interesting ways with the smooth setting.

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Section: •1 the Normal Euler Numbermentioning

confidence: 99%

Section: •2 Lagrangian Cobordismsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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