homotopy

(redirected from Homotopical)

homotopy

[hō′mäd·ə·pē]
(mathematics)
Between two mappings of the same topological spaces, a continuous function representing how, in a step-by-step fashion, the image of one mapping can be continuously deformed onto the image of the other.
References in periodicals archive ?
Hosted at one of the major centres for algebraic topology in the world and supervised by a world leader in homotopical group theory, The project will have a substantial impact on the er~s career by deepening and broadening his research expertise, Especially concerning p-compact groups and cohomology of finite groups; By significantly broadening his research network; And by solidifying his position as a trailblazer and leader in applying techniques from string topology to tackle difficult problems in group homology and cohomology.
Ultimately, he gives a homotopical interpretation of a deep relationship between operads and Grothendieck-TeichmEller groups.
Embryologically, it arises in the brain of placental mammals as an elongated midline structure composed of 2-3 x 108 fibers horizontal interconnecting homotopical and heterotopical cortical areas (2,23,24).
Its homotopical tools should be similarly non-reversible, and homotopy constructions occur here in a directed version, which gives rise to new "shapes" with elegance that is strengthened by the fact that such constructions are determined by universal properties.
Seade (mathematics, UNAM, Mexico) and Teissier (Institut Mathematique de Jussieu, Paris) have edited these papers on such subjects as the Join Theorem for polar weighted homogenous singularities, homotopical variation and Jacobian curves for normal complex surfaces.
QD67] Daniel Quillen, Homotopical Algebra, Lectures Notes 43, Springer-Verlag, Berlin, 1967.
Recently, an extension of type theory with homotopical concepts such as univalence is gaining traction because it allows for the first time to marry together expected principles of equality.
Homotopical Algebra, Lecture Notes in Math, 43, Springer, 1967.