Advances in Algebraic Topology: Combination of Geometric and Algebraic Methods
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".
Deadline for manuscript submissions: closed (30 September 2021) | Viewed by 2204
Special Issue Editor
Special Issue Information
Dear Colleagues,
One of the most classical problems of Algebraic Topology is the computation of homotopy groups of spheres. Progress in this direction was initially achieved by L.S. Pontryagin, whose construction translated this problem into a geometric one, namely the computation of cobordism groups of embedded framed manifolds. Later, R. Thom inverted and extended this connection between algebra (Algebraic Topology) and geometry (Differential Topology). Today, this connection is known as the Pontryagin–Thom construction.
This Special Issue will cover the fascinating connections between algebra and geometry. The first paper extends the Pontryagin–Thom construction to the cobordism theory of singular maps with a restricted set of allowed local singularities.
Potential topics of the issue include, but are not limited to, the following:
- Global singularity theory problems;
- Thom polynomials;
- Geometric cohomology operations;
- Proving classical results on homotopy groups geometrically, e.g., Freudenthal theorem, EHP sequence, double suspension in homotopy groups of spheres;
- Multiple point formulas for singular maps;
- Bar constructions and Morin singularities.
Prof. Dr. Andras Szucs
Guest Editor
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Keywords
- Pontryagin–Thom construction
- Cobordisms
- Immersions
- Singular maps
- Singularity locus
- Multiple points set
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