Mathematical and Molecular Topology

Dear Colleagues,

This Special Issue, "Mathematical and Molecular Topology", is open for submissions and welcomes papers from a broad interdisciplinary area, since topology is concerned with the properties of objects that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending. One of the oldest problems in topology is The Seven Bridges of Königsberg.

Topology naturally finds application in all fields of engineering, physical sciences, life sciences, social sciences, medicine, business and even arts. The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together.

In about 1750, Euler stated the polyhedron formula, V − E + F = 2 (where V, E, and F respectively indicate the number of vertices, edges, and faces of the polyhedron), which may be regarded as the first theorem, signaling the birth of topology.

Subjects included in topology are graph theory and algebraic topology. MSC 2010 subjects related to topology include the following: Number theory (with Density, gaps, topology and Relations with algebraic geometry and topology); Algebraic geometry (with Topology of surfaces—Donaldson polynomials, Seiberg–Witten invariants and Topology of real algebraic varieties); Category theory & homological algebra (for categories in topology); K-theory (for obstructions from topology); Group theory and generalizations (for other groups related to topology); Topological groups & Lie groups; Real functions (for elementary topology of the line); Several complex variables and analytic spaces (for Topology of analytic spaces); Dynamical systems and ergodic theory (for Topology in relation with holomorphic dynamical systems and Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology); Functional analysis (for Embeddings of discrete metric spaces into Banach spaces; applications in topology, Hilbert and pre-Hilbert spaces: geometry and topology, Noncommutative topology, and Methods of algebraic topology in functional analysis); Quantum theory (for Feynman integrals and graphs; applications of algebraic topology); Game theory, economics, finance, and other social and behavioral sciences (for Games involving topology); and finally Biology and other natural sciences (for Molecular structure—graph-theoretic methods, methods of differential topology and alike). Finally, three sections of MSC are almost entirely devoted to or build upon topology: General topology (54-XX), Algebraic topology (55-XX) and Manifolds and cell complexes (57-XX).

Prof. Dr. Lorentz Jäntschi
Dr. Mihaela Tomescu
Guest Editors

Manuscript Submission Information

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• algebraic topology
• clopen sets
• cohomology
• compactness
• connectedness
• continuity
• differential topology
• euclidean spaces
• geometric topology
• graph theory
• grothendieck topologies
• homeomorphisms
• homology
• homotopy
• manifolds
• metric spaces
• molecular topology
• point-set topology
• surgery theory
• topological invariants