{"product_id":"natural-operations-in-differential-geometry-von-ivan-kolar-peter-w-michor-jan-slovak","title":"Natural Operations in Differential Geometry","description":"The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642081491\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540562351\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642081491","offer_id":39437078626397,"sku":"9783642081491","price":128.39,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783540562351","offer_id":51344984006,"sku":"9783540562351","price":128.39,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/dd425cb4-dc85-477e-8ffb-085733c52e1f.jpg?v=1772173873","url":"https:\/\/shop.autorenwelt.de\/products\/natural-operations-in-differential-geometry-von-ivan-kolar-peter-w-michor-jan-slovak","provider":"Autorenwelt Shop","version":"1.0","type":"link"}