# Manifolds

### Some articles on manifolds, manifold:

Calculus On Manifolds (book)
... Michael Spivak's Calculus on Manifolds A Modern Approach to Classical Theorems of Advanced Calculus (1965, ISBN 0-8053-9021-9) is a short text treating analysis in several variables in Euclidean spaces and ... forms and in the context of differentiable manifolds embedded in Euclidean space ... Calculus on Manifolds aims to present the topics of vector analysis in the manner that they are seen by a working mathematician, yet simply and selectively ...
Surgery Exact Sequence
... exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in dimension ... The surgery structure set of a compact -dimensional manifold is a pointed set which classifies -dimensional manifolds within the homotopy type of ... one has to proceed case by case, for each manifold it is a unique task to determine the surgery exact sequence, see some examples below ...
Theodore James Courant
... In particular, he made seminal contributions to the study of Dirac manifolds, which generalize both symplectic manifolds and Poisson manifolds, and are ...
Classification Of Manifolds - Maps Between Manifolds
... From the point of view of category theory, the classification of manifolds is one piece of understanding the category it's classifying the objects ... The other question is classifying maps of manifolds up to various equivalences, and there are many results and open questions in this area ... is for some purposes "self maps of low dimensional manifolds", and for other purposes "low codimension" ...
Classification Of Manifolds - Dimension 4: Exotic
... For more details on this topic, see 4-manifold. 4-dimensional manifolds are the most unusual they are not geometrizable (as in lower dimensions), and surgery works topologically, but not differentiably ... Since topologically, 4-manifolds are classified by surgery, the differentiable classification question is phrased in terms of "differentiable structures" "which (topological) 4-man ...