In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another...

after K. Algebraic L-theory, also known as "Hermitian K-theory", is important in surgery theory. One can define L-groups for any ring with involution R:...

manifolds and differentiable manifolds coincide. The two basic questions of surgery theory are whether a topological space with n-dimensional Poincaré duality...

In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a...

be studied using the surgery theory program. In dimension 4 and below (topologically, in dimension 3 and below), surgery theory does not work. Indeed...

patients Surgery (journal), a medical journal Surgery theory, a mathematical operation used in topology; two special cases are: Dehn surgery Hyperbolic...

Set theory — Shape theory — Small cancellation theory — Spectral theory — Stability theory — Stable theory — Sturm–Liouville theory — Surgery theory — Twistor...

topology due to William Browder which is of fundamental importance in surgery theory. Given a Poincaré complex X (more geometrically a Poincaré space), a...

Orr, K (2000), "A survey of applications of surgery to knot and link theory", Surveys on Surgery Theory: Papers Dedicated to C.T.C. Wall, Annals of mathematics...

theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic topology, cobordism theories...

encompassed modern oral surgery, cosmetic surgery, sutures, ligatures, amputations, tonsillectomies, mastectomies, cataract surgeries, lithotomies, hernia...

structure; high-dimensional manifolds are classified algebraically, by surgery theory. "Low dimensions" means dimensions up to 4; "high dimensions" means...

{\displaystyle L_{4k+2}} , and thus analogous to the other invariants from L-theory: the signature, a 4 k {\displaystyle 4k} -dimensional invariant (either...

Gender-affirming surgery (GAS) is a surgical procedure, or series of procedures, that alters a person's physical appearance and sexual characteristics...

pieces. Handlebodies play an important role in Morse theory, cobordism theory and the surgery theory of high-dimensional manifolds. Handles are used to...

In the mathematical surgery theory the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold...

smoothable topological constructions, such as smooth surgery theory or the construction of cobordisms. Morse theory is an important tool which studies smooth manifolds...

theory Spectral theory String theory Sturm-Liouville theory Surgery theory Teichmüller theory Theory of equations Theory of statistics Topos theory Transcendental...

can be analyzed by surgery theory similarly to manifolds, and failure to be a manifold is a local obstruction, as in surgery theory. Differential spaces...

mathematical field of geometric topology, among the techniques known as surgery theory, the process of plumbing is a way to create new manifolds out of disk...

characteristic 2 (applied in knot theory and surgery theory) in topology, the Hasse–Arf theorem in ramification theory, Arf semigroups and Arf rings. Cahit...

(4k + 2)-dimensional manifold M which is framed except at a point. In surgery theory, for any 4 k + 2 {\displaystyle 4k+2} -dimensional normal map ( f ,...

{\displaystyle (-)^{n}} -quadratic forms, particularly in the context of surgery theory. There is the related notion of ε-symmetric forms, which generalizes...

fundamental class [ M ] . {\displaystyle [M].} Poincaré spaces are used in surgery theory to analyze and classify manifolds. Not every Poincaré space is a manifold...

Normal mapping in 3D computer graphics Normal invariants in mathematical surgery theory Normal matrix in linear algebra Normal operator in functional analysis...

point of view of surgery theory, this is "high (co)dimension", unlike codimension 2 which is the knotting dimension, as in knot theory. It is studied categorically...

J. H. C. Whitehead. The Whitehead torsion is important in applying surgery theory to non-simply connected manifolds of dimension > 4: for simply-connected...

for which he received the Fields Medal and is a fundamental result in the theory of high-dimensional manifolds. For a start, it almost immediately proves...

in the development of surgery theory. In fact, these calculations can be formulated in a modern language in terms of the surgery exact sequence as indicated...

construction, it is the technical heart of cobordism theory, and the starting point for surgery theory. The finite-dimensional version of the transversality...