Download Grassmannians and Gauss Maps in Piecewise-Linear and by Norman Levitt PDF

By Norman Levitt

The booklet explores the potential of extending the notions of "Grassmannian" and "Gauss map" to the PL type. they're exceptional from "classifying area" and "classifying map" that are basically homotopy-theoretic notions. The analogs of Grassmannian and Gauss map outlined comprise geometric and combinatorial details. crucial purposes contain attribute category concept, smoothing concept, and the life of immersion satifying yes geometric standards, e.g. curvature stipulations. The e-book assumes wisdom of uncomplicated differential topology and package thought, together with Hirsch-Gromov-Phillips thought, in addition to the analogous theories for the PL classification. The paintings will be of curiosity to mathematicians desirous about geometric topology, PL and PD features of differential geometry and the geometry of polyhedra.

Show description

Read Online or Download Grassmannians and Gauss Maps in Piecewise-Linear and Piecewise-Differential Topology PDF

Best geometry and topology books

Arithmetic Algebraic Geometry. Proc. conf. Trento, 1991

This quantity comprises 3 lengthy lecture sequence via J. L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their issues are respectively the relationship among algebraic K-theory and the torsion algebraic cycles on an algebraic style, a brand new method of Iwasawa idea for Hasse-Weil L-function, and the purposes of arithemetic geometry to Diophantine approximation.

The Theory Of The Imaginary In Geometry: Together With The Trigonometry Of..

Книга the speculation Of The Imaginary In Geometry: including The Trigonometry Of. .. the idea Of The Imaginary In Geometry: including The Trigonometry Of The Imaginary Книги Математика Автор: J. L. S. Hatton Год издания: 2007 Формат: djvu Издат. :Kessinger Publishing, LLC Страниц: 220 Размер: 6,1 Mb ISBN: 0548805520 Язык: Английский0 (голосов: zero) Оценка:J.

Extra resources for Grassmannians and Gauss Maps in Piecewise-Linear and Piecewise-Differential Topology

Sample text

M } ] : L (M) E (M;R). 19 defined for M bounds o r i e n t a b l y , i . e . q, in M = @W. ) some Under t h i s neighborhood of M. the s i g n a t u r e of the o r i e n t e d m a n i f o l d There are then two is merely the usual a l g e b r a i c - t o p o l o g i c a l s i g n a t u r e of a m a n i f o l d - w i t h - b o u n d a r y i . e . form in (If We assume W be equipped w i t h a Riemannian m e t r i c i s o m e t r i c obvious " c a n d i d a t e s " f o r The f i r s t 4i-i M o r i e n t e d Riemannian ( 4 i - 1 ) - m a n i f o l d s 2J-dimensional r a t i o n a l the s i g n a t u r e of homology.

6 to the l a r g e r c o n t e x t of A-homology m a n i f o l d s . 14 Corollary. Given an i - d i m e n s i o n a l c h a r a c t e r i s t i c class A-homology n - m a n i f o l d s , t h e r e e x i s t s a l o c a l representing for o r d e r e d formula c. We c l a i m t h a t t h i s extension is e a s i l y achieved. It r e a d i l y be seen by the reader t h a t the basic d e f i n i t i o n s s-cell c complex, s - b l o c k b u n d l e , s - c e l l , etc. will s-ball, - may be mimicked in c c n t e x t a p p r o p r i a t e to the study of A-homology m a n i f o l d s .

21 than a l o c a l - o r d e r e d formula. However, d e s p i t e i t s attractive c a n o n i c i t y , t h i s formula has not been made " c o m b i n a t o r i a l " in the sense t h a t a d i r e c t a l g o r i t h m f o r computing i t purely from the combi4i -I n a t o r i a l data of is not y e t known. Indeed, the t r a d i t i o n a l difficulties in a c t u a l l y computing the ~ - i n v a r i a n t of a smooth Riemannian m a n i f o l d c e r t a i n l y seem to p e r s i s t in t h i s c o n t e x t as well as f a r as is c u r r e n t l y known.

Download PDF sample

Download Grassmannians and Gauss Maps in Piecewise-Linear and by Norman Levitt PDF
Rated 4.62 of 5 – based on 38 votes