Results 1 to 10 of about 140,252 (207)
Applied Mathematics, 2020 Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have been applied to synthetic molecular design. Mathematics
Tahmineh Azizi, Jacob Pichelmeyer
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The T-algebra spectral sequence: Comparisons and applications [PDF]
, 2014 In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as G-spaces and E_n-ring spectra.
Noel, Justin
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Mathematical Models of Abstract Systems: Knowing abstract geometric forms [PDF]
, 2013 Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they ...
Marquis, Jean-Pierre
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An Inquiry into the Practice of Proving in Low-Dimensional Topology [PDF]
, 2015 The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role.
A. Fomenko +17 more
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Non-isotopic Heegaard splittings of Seifert fibered spaces [PDF]
, 2006 We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3-manifolds. Combining this invariant with a theorem of R Weidmann, proved here in the appendix, we show that a closed, totally orientable Seifert ...
Bachman +9 more
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Implications of the Ganea Condition [PDF]
, 2004 Suppose the spaces X and X cross A have the same Lusternik-Schnirelmann category: cat(X cross A)= cat(X). Then there is a strict inequality cat(X cross (A halfsmash B)) < cat (X) + cat(A halfsmash B) for every space B, provided the connectivity of A is ...
Berstein +10 more
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On the relationship between topological and geometric defects
, 2017 The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices.
Griffin, Sinead M., Spaldin, Nicola A.
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Sutured Heegaard diagrams for knots [PDF]
, 2006 We define sutured Heegaard diagrams for null-homologous knots in 3-manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a Murasugi sum.
Burde +11 more
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Dyer-Lashof-Cohen operations in Hochschild cohomology [PDF]
, 2005 We give explicit formulae for operations in Hochschild cohomology which are analogous to the operations in the homology of double loop spaces. As a corollary we obtain that any brace algebra in finite characteristic is always a restricted Lie algebra ...
Tourtchine, Victor
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The Gromov width of complex Grassmannians [PDF]
, 2005 We show that the Gromov width of the Grassmannian of complex k-planes in C^n is equal to one when the symplectic form is normalized so that it generates the integral cohomology in degree 2. We deduce the lower bound from more general results. For example,
Biran +7 more
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