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The prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) collection of prime 3-manifolds. A manifold is prime if it cannot be presented as a connected sum of more than one manifold, none of which is the sphere of the same dimension.
In particular if the surgery coefficient is of the form /, then the surgered 3-manifold is still the 3-sphere. If M {\displaystyle M} is the 3-sphere, L {\displaystyle L} is the right-handed trefoil knot , and the surgery coefficient is + 1 {\displaystyle +1} , then the surgered 3-manifold is the Poincaré dodecahedral space .
In medicine, a sign, symptom, or medical condition that leads to the recommendation of a treatment, test, or procedure. (NCI) Informed consent. A process in which a person is given important facts about a medical procedure or treatment, a clinical trial, or genetic testing before deciding whether or not to participate. It also includes ...
The study of maps of 1-dimensional manifolds are a non-trivial area. For example: Groups of diffeomorphisms of 1-manifolds are quite difficult to understand finely [2] Maps from the circle into the 3-sphere (or more generally any 3-dimensional manifold) are studied as part of knot theory.
Once a small subfield of geometric topology, the theory of 3-manifolds has experienced tremendous growth in the latter half of the 20th century. The methods used tend to be quite specific to three dimensions, since different phenomena occur for 4-manifolds and higher dimensions.
Pharmacotherapy, also known as pharmacological therapy or drug therapy, is defined as medical treatment that utilizes one or more pharmaceutical drugs to improve ongoing symptoms (symptomatic relief), treat the underlying condition, or act as a prevention for other diseases (prophylaxis). [1]
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Medical protocol may refer to: Medical guideline, for a medical treatment Medical protocol, a set of rules followed by an emergency medical technician, nurse, physician, therapist, etc. Clinical protocol, a method in a clinical trial or medical research study