Titlebook: Research Directions in Symplectic and Contact Geometry and Topology; Bahar Acu,Catherine Cannizzo,Lisa Traynor Book 2021 The Author(s) and

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2364-5733 e of mathematicians.Serves as an introduction to important qThis book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past fe

丰富

,A Polyfold Proof of Gromov’s Non-squeezing Theorem,work of Hofer-Wysocki-Zehnder to give proofs involving moduli spaces of pseudoholomorphic curves that are relatively short and broadly accessible, while also fully detailed and rigorous. We moreover review the polyfold description of Gromov-Witten moduli spaces in the relevant case of spheres with m

myelography

Synthesize

Action-Angle and Complex Coordinates on Toric Manifolds,an .-action. We summarize the construction of . as a symplectic quotient of ., the .-actions on . and their moment maps, and Guillemin’s Kähler potential on .. While the theories presented in this paper are for compact toric manifolds, they do carry over for some noncompact examples as well, such as

原告

An Introduction to Weinstein Handlebodies for Complements of Smoothed Toric Divisors, using explicit coordinates and a simple example. This article also serves to welcome newcomers to Weinstein handlebody diagrams and Weinstein Kirby calculus. Finally, we include several complicated examples at the end of the article to showcase the algorithm and the types of Weinstein Kirby diagram

congenial

Constructions of Lagrangian Cobordisms,an knots. There are some known “elementary” building blocks for Lagrangian cobordisms that are smoothly the attachment of 0- and 1-handles. An important question is whether every pair of non-empty Legendrians that are related by a connected Lagrangian cobordism can be related by a ribbon Lagrangian

Omniscient

前兆

火车车轮

On Khovanov Homology and Related Invariants,and . foam homology theories. Inspired by Alishahi and Dowlin’s bounds for the unknotting number coming from Khovanov homology and relying on spectral sequence arguments, we produce bounds on the alternation number of a knot. Lee and Bar-Natan spectral sequences also provide lower bounds on Turaev genus.