arXiv subjects

Federico Salmoiraghi

Publications and source records attributed to Federico Salmoiraghi.

4 recordsLinked to original sources

arXiv2026

New Anosov flows via bicontact structures

We present a new approach to hyperbolic plugs, via a construction of bicontact plugs on 3-manifolds with boundary that are surface bundles over the circle. The boundary components are quasi transverse tori, and we prove a gluing theorem that allows us to produce closed manifolds carrying new transitive Anosov flows. We show that a toroidal manifold produced by gluing two copies of the figure eight knot complement may carry many nonequivalent Anosov flows, and likewise a manifold composed of a figure eight complement and a trefoil complement. We further show that certain generalized Handel--Thurston surgeries can be realized as sequences of Goodman--Fried surgeries and produce new examples of different surgery sequences resulting in the same Anosov flow.

math.DS↗

arXiv2024

Surgery on Anosov flows using bi-contact geometry

Using bi-contact geometry, we define a new type of Dehn surgery on an Anosov flow with orientable weak invariant foliations. The Anosovity of the new flow is strictly connected to contact geometry and the Reeb dynamics of the defining bi-contact structure. This approach gives new insights into the properties of the flows produced by Goodman surgery and clarifies under which conditions Goodman's construction yields an Anosov flow. Our main application gives a necessary and sufficient condition to generate a contact Anosov flow by Foulon-Hasselblatt Legendrian surgery on a geodesic flow. In particular we show that this is possible if and only if the surgery is performed along a simple closed geodesic. As a corollary we have that any (positive) skewed R-covered Anosov flow obtained by surgery on a closed orbit of a geodesic flow is orbit equivalent to a (positive) contact Anosov flow.

math.GT↗

arXiv2023

Goodman surgery and projectively Anosov flows

We introduce a generalization of Goodman surgery to the category of projectively Anosov flows. This construction is performed along a knot that is simultaneously Legendrian and transverse for a supporting bi-contact structure. If the flow is Anosov there is a particular class of supporting bi-contact structures that induce Lorentzian metrics satisfying Barbot's criterion of hyperbolicity. Foulon and Hasselblatt construct new contact Anosov flows by surgery from a geodesic flow. We generalize their result showing that in any contact Anosov flow there is a family of Legendrian knots that can be used to produce new contact Anosov flows by surgery. Outside of the realm of Anosov flows we generate new examples of projectively Anosov flows on hyperbolic 3-manifolds. These flows contain an invariant submanifold of genus g>0. We also give some application to contact geometry: we interpret the bi-contact surgery in terms of classic contact-Legendrian surgery and admissible-inadmissible transverse surgery and we deduce some (hyper)tightness result for contact and transverse surgeries.

math.DS↗

arXiv2020

Equivalence of Contact Gluing Maps in Sutured Floer Homology

We show that the contact gluing map of Honda, Kazez, and Matic has a natural algebraic description. In particular, we establish a conjecture of Zarev, that his gluing map on sutured Floer homology is equivalent to the contact gluing map.

math.GT↗