scholarly journals Instanton Floer homology and contact structures

2015 ◽  
Vol 22 (2) ◽  
pp. 939-978 ◽  
Author(s):  
John A. Baldwin ◽  
Steven Sivek
Keyword(s):  
Floer Homology ◽  
Contact Structures

Heegaard Floer homology and contact structures

2005 ◽  
Vol 129 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Peter Ozsváth ◽  
Zoltán Szabó
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Contact Structures ◽  
Heegaard Floer

scholarly journals Sutured ECH is a natural invariant

2022 ◽  
Vol 275 (1350) ◽  
Author(s):  
Çağatay Kutluhan ◽  
Steven Sivek ◽  
C. Taubes
Keyword(s):  
Floer Homology ◽  
Contact Structures ◽  
Contact Homology ◽  
Compactness Result ◽  
Content Type ◽  
Embedded Contact Homology ◽  
Manifold With Boundary

We show that sutured embedded contact homology is a natural invariant of sutured contact 3 3 -manifolds which can potentially detect some of the topology of the space of contact structures on a 3 3 -manifold with boundary. The appendix, by C. H. Taubes, proves a compactness result for the completion of a sutured contact 3 3 -manifold in the context of Seiberg–Witten Floer homology, which enables us to complete the proof of naturality.

Autonomous Geometrical Mechanics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Contact Structure ◽  
Invariant Tori ◽  
Time Dependent ◽  
Contact Structures ◽  
Natural Setting ◽  
Adiabatic Invariance ◽  
Jet Bundle ◽  
Integrability Theorem ◽  
Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

scholarly journals Contact structures and reducible surgeries

2015 ◽  
Vol 152 (1) ◽  
pp. 152-186 ◽  
Author(s):  
Tye Lidman ◽  
Steven Sivek
Keyword(s):  
Contact Structures ◽  
Surgery Theory ◽  
Contact Topology ◽  
Exceptional Surgery ◽  
Genus 2 ◽  
Cabling Conjecture

We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus$g$must have slope$2g-1$, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.

scholarly journals On contact structures of real and complex manifolds

1963 ◽  
Vol 15 (3) ◽  
pp. 227-252 ◽  
Author(s):  
Seizi Takizawa
Keyword(s):  
Contact Structures ◽  
Complex Manifolds

scholarly journals Microfluidic Optical Shutter Flexibly x-y Actuated via Electrowetting-on-Dielectrics with <20 ms Response Time

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Henning Fouckhardt ◽  
Johannes Strassner ◽  
Carina Heisel ◽  
Dominic Palm ◽  
Christoph Doering
Keyword(s):  
Optical Properties ◽  
Response Time ◽  
Visible Spectral Range ◽  
Contact Structures ◽  
Light Path ◽  
Cell Type ◽  
Electrically Conductive ◽  
Droplet Movement ◽  
In Series ◽  
Optical Shutter

Tunable microoptics deals with devices of which the optical properties can be changed during operation without mechanically moving solid parts. Often a droplet is actuated instead, and thus tunable microoptics is closely related to microfluidics. One such device/module/cell type is an optical shutter, which is moved in or out of the path of the light. In our case the transmitting part comprises a moving transparent and electrically conductive water droplet, embedded in a nonconductive blackened oil, that is, an opaque emulsion with attenuation of 30 dB at 570 nm wavelength over the 250 μm long light path inside the fluid (15 dB averaged over the visible spectral range). The insertion loss of the cell is 1.5 dB in the “open shutter” state. The actuation is achieved via electrowetting-on-dielectrics (EWOD) with rectangular AC voltage pulses of 2·90 V peak-to-peak at 1 kHz. To flexibly allow for horizontal, vertical, and diagonal droplet movement in the upright x-y plane, the contact structures are prepared such that four possible stationary droplet positions exist. The cell is configured as two capacitors in series (along the z axis), such that EWOD forces act symmetrically in the front and back of the 60 nl droplet with a response time of <20 ms.

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