92 citations · 273 across the 36 of their papers we have counts for
7 papers · 1 filter
Combinatorial Morse flows are hard to find
Liviu I. Nicolaescu
We investigate the probability of detecting combinatorial Morse flows on a simplicial complex via a random search. We prove that it is really small, in a quantifiable way.
On the total curvature of semialgebraic graphs
Liviu I. Nicolaescu
We define the total curvature of a semialgebraic embedding of a graph in the 3-dimensional Euclidean space. We prove that it satisfies a Chern-Lashof type inequality and we describ…
Tame Flows
Liviu I. Nicolaescu
The tame flows are ``nice'' flows on ``nice'' spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow on pfaffian set $X…
Morse functions statistics
Liviu I. Nicolaescu
We answer a question of V.I. Arnold concerning the growth rate of the number of Morse functions on the two sphere.
Counting Morse functions on the 2-sphere
Liviu I. Nicolaescu
This paper was motivated by work of Arnold where he explains how to count "snakes", i.e. Morse functions on the real axis with prescribed behavior at infinity. This leads immediate…
Seiberg-Witten invariants of rational homology spheres
Liviu I. Nicolaescu
We prove that the Seiberg-Witten invariants of a rational homology sphere are determined in a very explicit fashion by the Casson-Walker invariant and the Reidemeister torsion