In the paper, smooth functions with non-degenerate critical points on a smooth compact
surface with boundary are considered. Firstly, it is shown that these functions are …

We investigate the topological properties, structures, and classifications of the Morse flows
with fixed points on the boundary of three-dimensional manifolds. We construct a complete …

This paper focuses on the problem of topological equivalence of functions with isolated
critical points on the boundary of a compact surface $ M $ which are also isolated critical …

arxiv:1603.00582v2 [math.GT] 6 Nov 2017 Page 1 Tye Lidman Ciprian Manolescu THE
EQUIVALENCE OF TWO SEIBERG-WITTEN FLOER HOMOLOGIES arxiv:1603.00582v2 [math.GT] …

We consider simple functions with nondegenerate singularities on smooth compact oriented
surfaces with boundary. The relationship between the optimality and polarity of Morse …

We prove an analog of the Morse theorem in the case where the critical point belongs to the
boundary of an n-dimensional manifold and find the least number of critical points for the …

We characterize the absolute continuity of the law and the Malliavin-Sobolev regularity of
random nodal volumes associated with smooth Gaussian fields on generic $\mathcal {C} …

We investigate topological properties of simple Morse functions with 4 critical points on
immersed 2-spheres. To classify such functions, dual graph of immersion and Reeb graphs …

In signal processing, a signal is a function. Conceptually, replacing a function by its graph,
and extending this approach to a more abstract setting, we define a signal as a submanifold …

We study the moduli space of handlebodies diffeomorphic to (D n+ 1× S n)♮ g, that is, the
classifying space BDiff ((D n+ 1× S n)♮ g, D 2 n) of the group of diffeomorphisms that restrict …