Topology change of level sets in Morse theory
نویسندگان
چکیده
منابع مشابه
C 0-topology in Morse Theory
Let f be a Morse function on a closed manifold M , and v be a Riemannian gradient of f satisfying the transversality condition. The classical construction (due to Morse, Smale, Thom, Witten), based on the counting of flow lines joining critical points of the function f associates to these data the Morse complex M * (f, v). In the present paper we introduce a new class of vector fields (f-gradie...
متن کاملMorse theory, graphs, and string topology
In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph flows, using homotopy theoretic methods to construct a virtual fundamental class, and evaluating cohomology classes on this fundamental class. By using similar c...
متن کاملParameterized Morse theory in low-dimensional and symplectic topology
The first part of the talk will be a quick survey on the homotopy type of the group of Diffeomorphisms of a 3-manifold. Pioneering work was done by Hatcher and Ivanov in the late 70s and early 80s, computing this for Haken 3-manifolds and famously the Smale conjecture. Following Thurston, the natural question is whether Diff is homotopy equivalent to the group of isometries, for geometric 3-man...
متن کاملOn invariant sets topology
In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...
متن کاملStatistical Topology via Morse Theory Persistence and Nonparametric Estimation
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation procedure can then be evaluated using the bottleneck distance between the estimated persistent homology and the true persistent homology. The connection to sta...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 2020
ISSN: 0004-2080,1871-2487
DOI: 10.4310/arkiv.2020.v58.n2.a6