topology (point-set topology, point-free topology)
see also differential topology, algebraic topology, functional analysis and topological homotopy theory
Basic concepts
fiber space, space attachment
Extra stuff, structure, properties
Kolmogorov space, Hausdorff space, regular space, normal space
sequentially compact, countably compact, locally compact, sigma-compact, paracompact, countably paracompact, strongly compact
Examples
Basic statements
closed subspaces of compact Hausdorff spaces are equivalently compact subspaces
open subspaces of compact Hausdorff spaces are locally compact
compact spaces equivalently have converging subnet of every net
continuous metric space valued function on compact metric space is uniformly continuous
paracompact Hausdorff spaces equivalently admit subordinate partitions of unity
injective proper maps to locally compact spaces are equivalently the closed embeddings
locally compact and second-countable spaces are sigma-compact
Theorems
Analysis Theorems
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
(…)
C. T. C. Wall (ed. Andrew Ranicki), Surgery on compact Manifolds, Math. Surveys and Monographs 69 (1999) [pdf]
Rustam Sadykov, Elements of Surgery Theory, 2013 (pdf, pdf)
Andrew Ranicki: High-dimensional knot theory – Algebraic Surgery in Codimension 2, Monographs in Mathematics, Springer (1998, 2009) [doi:10.1007/978-3-662-12011-8, pdf]
(via surgery and algebraic K-theory and L-theory)
In relation to Hopf invariants:
See also:
Last revised on August 16, 2024 at 16:32:40. See the history of this page for a list of all contributions to it.