On families in differential geometry

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F13%3A%230000394" target="_blank" >RIV/47813059:19610/13:#0000394 - isvavai.cz</a>
Výsledek na webu
<a href="http://www.worldscientific.com/doi/abs/10.1142/S0219887813500424" target="_blank" >http://www.worldscientific.com/doi/abs/10.1142/S0219887813500424</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0219887813500424" target="_blank" >10.1142/S0219887813500424</a>

Jazyk výsledku
angličtina
Název v původním jazyce
On families in differential geometry
Popis výsledku v původním jazyce
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows one to work without introducing ad hoc spaces, by using the language of differential calculus over commutative algebras. An advantage of such an approach, based on the notion of sliceable structures on cylinders, is that the fundamental theorems of standard calculusare straightforwardly generalized to the context of families. As an example of that, we prove the universal homotopy formula.
Název v anglickém jazyce
On families in differential geometry
Popis výsledku anglicky
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows one to work without introducing ad hoc spaces, by using the language of differential calculus over commutative algebras. An advantage of such an approach, based on the notion of sliceable structures on cylinders, is that the fundamental theorems of standard calculusare straightforwardly generalized to the context of families. As an example of that, we prove the universal homotopy formula.

Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
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Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2013
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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