Algebraic Topology and Related Topics

Description

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. Front Matter ....Pages i-xiii The Homotopy Type of the Loops on \((n-1)\)-Connected \((2n+1)\)-Manifolds (Samik Basu)....Pages 1-25 Whitehead’s Asphericity Question and Its Relation to Other Open Problems (A. J. Berrick, J. A. Hillman)....Pages 27-49 Connective K-Theory and the Borsuk–Ulam Theorem (M. C. Crabb)....Pages 51-66 Torus Orbifolds with Two Fixed Points (Alastair Darby, Shintaro Kuroki, Jongbaek Song)....Pages 67-85 Arc Shift Number for Some Virtual Knots (K. Kaur, A. Gill, M. Prabhakar)....Pages 87-101 Exponents of \([\Omega ({\mathbb {S}}^{r+1}), \Omega (Y)]\) (Marek Golasiński, Daciberg Lima Gonçalves, Peter Wong)....Pages 103-122 Mayer–Vietoris Sequence for Differentiable/Diffeological Spaces (Norio Iwase, Nobuyuki Izumida)....Pages 123-151 Homological Infinity of 4D Universe for Every 3-Manifold (Akio Kawauchi)....Pages 153-176 Nielsen Theory on Nilmanifolds of the Standard Filiform Lie Group (Jong Bum Lee, Won Sok Yoo)....Pages 177-195 Lickorish-type Construction of Manifolds Over Simple Polytopes (Zhi Lü, Wei Wang, Li Yu)....Pages 197-213 KO-Groups of Stunted Complex and Quaternionic Projective Spaces (Aniruddha C. Naolekar, Ajay Singh Thakur)....Pages 215-221 The Vector Field Problem for Homogeneous Spaces (Parameswaran Sankaran)....Pages 223-264 On a Construction for the Generators of the Polynomial Algebra as a Module Over the Steenrod Algebra (Nguyễn Sum)....Pages 265-286 Stellar Stratifications on Classifying Spaces (Dai Tamaki, Hiro Lee Tanaka)....Pages 287-313