172 research outputs found
Topological field theory on r-spin surfaces and the Arf invariant
No full textWe give a combinatorial model for r-spin surfaces with parametrised boundary
based on Novak (2015). The r-spin structure is encoded in terms of
-valued indices assigned to the edges of a polygonal
decomposition. This combinatorial model is designed for our state sum
construction of two-dimensional topological field theories on r-spin surfaces.
We show that an example of such a topological field theory computes the
Arf-invariant of an r-spin surface as introduced in Geiges, Gonzalo (2012) and
Randal-Williams (2014). This implies in particular that the r-spin
Arf-invariant is constant on orbits of the mapping class group, providing an
alternative proof of that fact.Comment: v2: 52 pages, removed classification of mapping class group orbits as
suggested by referee, version to appear in Journal of Mathematical Physic
NEIGHBOURHOODS AND ISOTOPIES OF KNOTS IN Contact 3-manifolds
No full textWe prove a neighbourhood theorem for arbitrary knots in contact 3-manifolds. As an application we show that two topologically isotopic Legendrian knots in a contact 3-manifold become Legendrian isotopic after suitable stabilisations.MathematicsSCI(E)1ARTICLE4391-3979
A Legendrian surgery presentation of contact 3-manifolds
No full textWe prove that every closed, connected contact 3-manifold can be obtained from S-3 with its standard contact structure by contact (+/-1)-surgery along a Legendrian link. As a corollary, we derive a result of Etnyre and Honda about symplectic cobordisms (in a slightly stronger form).MathematicsSCI(E)0ARTICLE583-59813
The diffeotopy group of S-1 x S-2 via contact topology
No full textAs shown by Gluck in 1962, the diffeotopy group of S-1 x S-2 is isomorphic to Z(2) circle plus Z(2) circle plus Z(2). Here an alternative proof of this result is given, relying on contact topology. We then discuss two applications to contact topology: (i) it is shown that the fundamental group of the space of contact structures on S-1 x S-2, based at the standard tight contact structure, is isomorphic to Z; (ii) inspired by previous work of Fraser, an example is given of an integer family of Legendrian knots in S-1 x S-2#S-1 x S-2 (with its standard tight contact structure) that can be distinguished with the help of contact surgery, but not by the classical invariants (topological knot type, Thurston-Bennequin invariant, and rotation number).http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000280156000012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)7ARTICLE41096-111214
E-8-plumbings and exotic contact structures on spheres
No full textMathematicsSCI(E)2ARTICLE713825-383
Contact structures on principal circle bundles
No full textWe describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary, it is shown that if the trivial circle bundle over a given base manifold carries an invariant contact structure, then so do all circle bundles over that base. In particular, all circle bundles over 4-manifolds admit invariant contact structures. We also discuss the Bourgeois construction of contact structures on odd-dimensional tori in this context, and we relate our results to recent work of Massot, Niederkruger and Wendl on weak symplectic fillings in higher dimensions.MathematicsSCI(E)1ARTICLE1189-12024
Generalised spin structures on 2-dimensional orbifolds
No full textGeneralised spin structures, or r -spin structures, on a 2-dimensional orbifold Σ are r -fold fibrewise connected coverings (also called r-th roots) of its unit tangent bundle ST6. We investigate such structures on hyperbolic orbifolds. The conditions on r for such structures to exist are given. The action of the diffeomorphism group of Σ on the set of r -spin structures is described, and we determine the number of orbits under this action and their size. These results are then applied to describe the moduli space of taut contact circles on left-quotients of the 3-dimensional geometry (SL2)~
- …
