Mayer Vietoris sequence for persistent homology

Download

index.pdf

Date

2018

Author

Yılmaz, Yağmur

Metadata

Show full item record

Item Usage Stats

367
views

130
downloads

Persistent homology is an algebraic method for understanding topological features of discrete objects or data (finite set of points with metric defined on it). In algebraic topology, the Mayer Vietoris sequence is a powerful tool which allows one to study the homology groups of a given space in terms of simpler homology groups of its subspaces. In this thesis, we study to what extent does persistent homology benefit from Mayer Vietoris sequence.

Subject Keywords

Holonomy groups., Algebraic topology., Sequences (Mathematics).

URI

http://etd.lib.metu.edu.tr/upload/12622408/index.pdf
https://hdl.handle.net/11511/27564

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Van Kampen theorem for persistent fundamental group Batan, Mehmet Ali; Pamuk, Mehmetcik; Department of Mathematics (2019) Persistent homotopy is one of the newest algebraic topology methods in order to understand and capture topological features of discrete objects or point data clouds (the set of points with metric defined on it). On the other hand, in algebraic topology, the Van Kampen Theorem is a great tool to determine fundamental group of complicated spaces in terms of simpler subspaces whose fundamental groups are already known. In this thesis, we show that Van Kampen Theorem is still valid for the persistent fundamenta...
On equivelar triangulations of surfaces Adıgüzel, Ebru; Pamuk, Semra; Department of Mathematics (2018) Persistent homology is an algebraic method for understanding topological features of discrete objects or data (finite set of points with metric defined on it). In algebraic topology, the Mayer Vietoris sequence is a powerful tool which allows one to study the homology groups of a given space in terms of simpler homology groups of its subspaces. In this thesis, we study to what extent does persistent homology benefit from Mayer Vietoris sequence.
Smooth manifolds with infinite fundamental group admitting no real projective structure Çoban, Hatice; Ozan, Yıldıray; Department of Mathematics (2017) In this thesis, we construct smooth manifolds with the infinite fundamental group Z_2*Z_2, for any dimension n>=4, admitting no real projective structure. They are first examples of manifolds in higher dimensions with infinite fundamental group admitting no real projective structures. The motivation of our study is the related work of Cooper and Goldman. They proved that RP^3#RP^3 does not admit any real projective structure and this is the first known example in dimension 3.
REFLECTION GROUP RELATIONS ARISING FROM CLUSTER ALGEBRAS Seven, Ahmet İrfan (American Mathematical Society (AMS), 2016-11-01) There is a well-known analogy between cluster algebras and Kac-moody algebras: roughly speaking, Kac-Moody algebras are associated with symmetrizable generalized Cartan matrices while cluster algebras correspond to skew-symmetrizable matrices. In this paper, we study an interplay between these two classes of matrices. We obtain relations in the Weyl groups of Kac-Moody algebras that come from mutation classes of skew-symmetrizable matrices. More precisely, we establish a set of relations satisfied by the re...
CLUSTER ALGEBRAS AND SEMIPOSITIVE SYMMETRIZABLE MATRICES Seven, Ahmet İrfan (American Mathematical Society (AMS), 2011-05-01) There is a particular analogy between combinatorial aspects of cluster algebras and Kac-Moody algebras: roughly speaking, cluster algebras are associated with skew-symmetrizable matrices while Kac-Moody algebras correspond to (symmetrizable) generalized Cartan matrices. Both classes of algebras and the associated matrices have the same classification of finite type objects by the well-known Cartan-Killing types. In this paper, we study an extension of this correspondence to the affine type. In particular, w...

Citation Formats

Y. Yılmaz, “Mayer Vietoris sequence for persistent homology,” M.S. - Master of Science, Middle East Technical University, 2018.