Algebraic Topology and Related Topics (eBook)

MAHENDER SINGH is an associate professor at the Indian Institute of Science Education and Research, Mohali, India. He earned his Ph.D. degree in Mathematics from the Harish-Chandra Research Institute, Allahabad, in 2010. His research interests include topology and algebra, particularly problems related to compact group actions on manifolds, equivariant maps, braid groups, automorphisms and cohomology of groups and quandles. YONGJIN SONG is a professor at the Department of Mathematics, Inha University, South Korea. He earned his Ph.D. degree in Topology from Ohio State University, USA. He was also associated with the Naval Academy of Mathematics, Ohio State University, and the Dalian University of Science and Technology. His research interests include algebraic topology, category theory, mapping class groups, various geometric groups, loop space structures and category structures and higher category theory. JIE WU is a professor at the Department of Mathematics, National University of Singapore. He has published over 70 research articles. His research interests are algebraic and geometric topology, homotopy theory, braid groups, modular representation theory and applied topology.

​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.