Algebraic Topology and Related Topics

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.

Chapter 1. Homological infinity of 4D universe for every 3-manifold.- Chapter 2. On the exponents of $[J(X), \Omega (Y)]$.- Chapter 3. Nielsen theory on the nilmanifold $\Gamma_{m+1}\backslash\mathrm{Heis}^{m+1}$ of the generalized Heisenberg group $\mathrm{Heis}^{m+1}$.- Chapter 4. Vector field problem for homogeneous spaces.- Chapter 5. Lickorish type classification of closed manifolds over simple polytopes.- Chapter 6. Stable and unstable stratifications on classifying spaces of acyclic categories.- Chapter 7. Equivariant cohomology of torus orbifolds with two vertices.- Chapter 8. Free torus actions on products of Milnor manifolds.- Chapter 9. The cohomology classes of a point and the diagonal in flag manifolds.- Chapter 10. On a construction for the generators of the polynomial algebra as a module over the Steenrod algebra.- Chapter 11. KO-groups of stunted complex and quaternionic projective spaces.- Chapter 12. Homotopy groups of (n-1)-connected (2n + 1)-manifolds.- Chapter 13. A note on the topology of polygonal spaces.- Chapter 14. Generalized unknotting number of virtual links.