arXiv subjects

Jovana Nikolić

Publications and source records attributed to Jovana Nikolić.

5 recordsLinked to original sources

arXiv2025

Restricted (2+1)-TQFTs supported by thickened and solid tori

A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distinguishable by quantum invariants.

math.GT↗

arXiv2024

A note on rational surgeries on a Hopf link

It is clear that every rational surgery on a Hopf link in $3$-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well known) result on the criterion for when rational surgery on a Hopf link gives the $3$-sphere.

math.GT↗

arXiv2021

A note on partial quasi-morphisms and products in Lagrangian Floer homology in cotangent bundles

We define partial quasi-morphisms on the group of Hamiltonian diffeomorphisms of the cotangent bundle using the spectral invariants in Lagrangian Floer homology with conormal boundary conditions, where the product compatible with the PSS isomorphism and the homological intersection product is lacking.

math.SG↗

arXiv2019

Spectral numbers and manifolds with boundary

We consider a smooth submanifold $N$ with a smooth boundary in an ambient closed manifold $M$ and assign a spectral invariant $c(α,H)$ to every singular homological class $α\in H_*(N)$ and a Hamiltonian $H$ defined on the cotangent bundle $T^*M$. We also derive certain properties of spectral numbers, for example we prove that spectral invariants $c_\pm(H,N)$ associated to the whole Floer homology $HF_*(H,N:M)$ of the submanifold $N$, are limits of the decreasing nested family of open sets.

math.SG↗

arXiv2017

Spectral Invariants in Lagrangian Floer homology of open subset

We define and investigate spectral invariants for Floer homology $HF(H,U:M)$ of an open subset $U\subset M$ in $T^*M$, defined by Kasturirangan and Oh as a direct limit of Floer homologies of approximations. We define a module structure product on $HF(H,U:M)$ and prove the triangle inequality for invariants with respect to this product. We also prove the continuity of these invariants and compare them with spectral invariants for periodic orbits case in $T^*M$.

math.SG↗