arXiv subjects

Ipsita Datta

Publications and source records attributed to Ipsita Datta.

6 recordsLinked to original sources

arXiv2025

Non-Simple knots in Contact 3-Manifolds

We present new families of examples of non-simple prime Legendrian and transversal knots in tight Lens spaces, which demonstrate that the botany of Legendrians in Lens space is rich. In fact, there are more non-isotopic Legendrians that are topologically isotopic to the $n$-twist knot in a Lens space $L(α, β)$ than in $S^3$. We also include connect sum formulas for rational variants of classical invariants, $\mathrm{tb}_\mathbb{Q}$, $\mathrm{rot}_\mathbb{Q}$, and $\mathrm{sl}_\mathbb{Q}$, which indicate that prime knots are the right playground to look for exotic behaviour.

math.GT↗

arXiv2025

An Invitation to Obstruction Bundle Gluing Through Morse Flow Lines

We adapt "Obstruction Bundle Gluing (OBG)" techniques from Hutchings and Taubes (arxiv: 0701300, 0705.2074) to Morse theory. We consider Morse function-metric pairs with gradient flowlines that have nontrivial yet well-controlled cokernels (i.e., the gradient flowlines are not transversely cut out). We investigate (i) whether these nontransverse gradient flowlines can be glued to other gradient flowlines and (ii) the bifurcation of gradient flowlines after we perturb the metric to be Morse-Smale. For the former, we show that certain three-component broken flowlines with total Fredholm index 2 can be glued to a one-parameter family of flowlines of the given metric if and only if an explicit (essentially combinatorial, and straightforward to verify) criterion is satisfied. For the latter, we provide a similar combinatorial criterion of when certain 2-level broken Morse flowlines of total Fredholm index 1 glue to index 1 gradient flowlines after perturbing the metric. Our primary example is the ``upright torus," which has a flowline between the two index-1 critical points.

math.SG↗

arXiv2023

Weinstein presentations for high-dimensional antisurgery

In this paper, we give an algorithm for describing the Weinstein presentation of Weinstein subdomains obtained by carving out regular Lagrangians. Our work generalizes previous work in dimension three and requires a novel Legendrian isotopy move (the ``boat move") that changes the local index of Reeb chords in a front projection. As applications, we describe presentations for certain exotic Weinstein subdomains and give explicit descriptions of $P$-loose Legendrians.

math.SG↗

arXiv2022

Contact homology and higher dimensional closing lemmas

We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the strong closing lemma holds for Reeb flows on ellipsoids. Our methods also apply to other Reeb flows, and we illustrate this for a class of examples introduced by Albers-Geiges-Zehmisch.

math.SG↗

arXiv2022

Lagrangian Cobordisms between Enriched Knot Diagrams

In this paper, we present new obstructions to the existence of Lagrangian cobordisms in $\mathbb{R}^4$ that depend only on the enriched knot diagrams of the boundary knots or links, using holomorphic curve techniques. We define enriched knot diagrams for generic smooth links. The existence of Lagrangian cobordisms gives a well-defined transitive relation on equivalence classes of enriched knot diagrams that is a strict partial order when restricted to exact enriched knot diagrams To establish obstructions we study $1$-dimensional moduli spaces of holomorphic disks with corners that have boundary on Lagrangian tangles - an appropriate immersed Lagrangian closely related to embedded Lagrangian cobordisms. We adapt existing techniques to prove compactness and transversality, and compute dimensions of these moduli spaces. We produce obstructions as a consequence of characterizing all boundary points of such moduli spaces. We use these obstructions to recover and extend results about ``growing" and ``shrinking" Lagrangian slices. We hope that this investigation will open up new directions in studying Lagrangian surfaces in $\mathbb{R}^4$.

math.SG↗

arXiv2020

A Polyfold proof of Gromov's Non-squeezing Theorem

We re-prove Gromov's non-squeezing theorem by applying Polyfold Theory to a simple Gromov-Witten moduli space. Thus we demonstrate how to utilize the 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 minimal energy and one marked point.

math.SG↗