Whitehead torsion

by John Willard Milnor

Publisher: [typescript] in [s.l.]

Written in English
Published: Downloads: 320
Share This

Edition Notes

StatementJ. Milnor.
ID Numbers
Open LibraryOL19578165M

§ Torsion for chain complexes § Whitehead torsion for CW-complexes § Reidemeister torsion § Torsion and lens spaces § The s-cobordism theorem § Projects for Chapter 11 Bibliography File Size: 1MB.   Thus, The Novikov Conjecture: Geometry and Algebra is not for the timid, the dabbler, or the dilettante. It is serious business and deals with a wealth of interesting and deep material from modern algebraic topology and differential geometry; here is a short sampling of topics: bordism, the signature, the Whitehead group, Whitehead torsion, s.   Introduction to Combinatorial Torsions by Vladimir Turaev, , available at Book Depository with free delivery : Vladimir Turaev. The author defines the higher Franz-Reidemeister torsion based on Volodin's K-theory and Borel's regulator map. He describes its properties and generalizations and studies the relation between the higher Franz-Reidemeister torsion and other torsions used in K-theory: Whitehead torsion and Ray-Singer torsion.

The torsion of a space is an element of the Whitehead group defined by the pair, where is a finite cellular space and the imbedding is a homotopy equivalence. Equivalently: The torsion is an element of the Whitehead group of the fundamental group. The torsion is invariant under cellular expansions and contractions and under cellular refinements. Whitehead torsion; Chemistry. Torsion angle; Medicine. Of bones, "torsion fracture" is another term for spiral fracture. Of organs, torsion refers to twisting, in particular twisting that interrupts the blood supply to that organ, e.g. splenic torsion, ovarian torsion, or testicular torsion. This book grew out of courses which I taught at Cornell University and the University of Warwick during and I wrote it because of a strong belief that there should be readily available a semi-historical and geoƯ metrically motivated exposition of J.H.C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was. If one takes the "quantum" view of the world, this is the "ultimate" Alexander polynomial, because it behaves well with respect to cabling, is calculable in linear .

We construct a higher Whitehead torsion map, using algebraic K-theory of spaces, and show that it satisfies the usual properties of the classical Whitehead : Wolfgang Steimle. This book gives an exposition of both the old and new results of spin and torsion effects on gravitational interactions with implications for particle physics, cosmology etc. Physical aspects are stressed and measurable effects in relation to other areas of physics are discussed. 7. On Whitehead torsion. 8. A few lines on L2-torsion. 1. Classical Setting Determinants of Matrices over Commutative Rings. Let R be a ring with unit. For an integer n≥1, denote by M nðRÞ the ring of n-by-n matrices over R and by GL nðRÞ its group of units. R*stands for GL 1ðRÞ. Suppose R is commutative. The determinant det:M. In particular the topological invariance of Whitehead torsion appears in Section The reader who is interested in R. D. Edwards' recent proof that every ANR is a Q-manifold factor should read the first four chapters and then (with the single exception of ) skip over to Chapters XIII and XIV.

Whitehead torsion by John Willard Milnor Download PDF EPUB FB2

Whitehead torsion is an algebraic K-theory invariant, which decides if an h-cobordism of high-dimensional manifolds is trivial. The classification of lens spaces via Whitehead torsion is. Algebraic and Geometric Surgery (Oxford Mathematical Monographs) Poincare duality, bundles, co-bordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations.

While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for Cited by: "Gustave Whitehead: First in Flight" presents new, compelling evidence to credit Gustave Whitehead, aka Gustav Weißkopf, as "first in powered flight" and inventor of the airplane.

This book reveals the fascinating truth about Whitehead's successful powered flights in Connecticut, more than two years before the Wrights flew at Kitty Hawk/5(23). Alfred North Whitehead () was an English mathematician [he is credited as co-writer with Bertrand Russell of Principia Mathematica] and philosopher, best known for developing Process wrote many other books such as Science and the Modern World,Religion in the Making, etc.

He begins Part II of the book with his famous statement about Plato: “The safest general 5/5(5). § Torsion for chain complexes § Whitehead torsion for CW-complexes § Reidemeister torsion § Torsion and lens spaces § The s-cobordism theorem § Projects for Chapter 11 Bibliography File Size: 3MB.

From an algebraic point of view, the torsion is a generalization of the notion of determinant. The most natural and general context to define the torsion would involve the Whitehead group and algebraic K-theory as in the very elegant and influential Milnor survey [72], but we did not adopt this more general point of view.

Instead we. A slim volume offering a fascinating glimpse of Antonin Dvorak's time spent in an Iowa village populated primarily by Czechs. The composer and his family spent the summer of in Spillville.

Hampl's elegant writing and rich imaginings render this book a must-read for any Iowan or any fan of Dvorak's music. The book includes a series of /5(5). Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. NOTES ON REIDEMEISTER TORSION ANDREW RANICKI Reidemeister torsion (R-torsion for short) is an algebraic topology invariant which takes values in the multiplicative group of the units of a commutative ring.

Although R-torsion has been largely subsumed in the more general theory of White-head torsion, it has retained a life of its own. REALIZING WHITEHEAD TORSION ELEMENTS In this section we study the realizability of Whitehead torsion elements and, in particular, we prove Theorem 1 which characterizes the dimension of a torsion element in terms of group extensions.

LEMMA If 0 # ¢o E Wh(rr,L) then 2 -Cited by:   These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones.

They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for. We study the Whitehead torsion of inertial h-cobordisms, continuing an investigation started in.

Of particular interest is a nested sequence of subsets of the Whitehead group, and a number of examples are given to show that these subsets are all different in general.

The main new results are TheoremTheoremTheorem Author: Bjørn Jahren, Sławomir Kwasik. The Whitehead conjecture is true if all sets are constructible. That this and other statements about uncountable abelian groups are provably independent of ZFC shows that the theory of such groups is very sensitive to the assumed underlying set theory.

See also. Free abelian group; Whitehead torsion; List of statements undecidable in ZFC. Analytic torsion (or Ray–Singer torsion) is an invariant of Riemannian manifolds defined by Daniel B.

Ray and Isadore M. Singer (, a, b) as an analytic analogue of Reidemeister torsion. Jeff Cheeger (, ) and Werner Müller () proved Ray and Singer's conjecture that Reidemeister torsion and analytic torsion are the.

Nicolaescu, Liviu I. (), Notes on the Reidemeister torsion, Online book Nicolaescu, Liviu I. (), The Reidemeister torsion of 3-manifolds, de Gruyter Studies in Mathematics, 30, Berlin: Walter de Gruyter & Co., pp.

xiv+, ISBNMR These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Stephen Smale (born J ) is an American mathematician, known for his research in topology, dynamical systems and mathematical was awarded the Fields Medal in and spent more than three decades on the mathematics faculty of the University of California, Berkeley (– and –).Alma mater: University of Michigan.

Cite this chapter as: Cohen M.M. () Whitehead Torsion in the CW Category. In: A Course in Simple-Homotopy Theory. Graduate Texts in Mathematics, vol Author: Marshall M.

Cohen. Cite this chapter as: Rutter J.W. () Whitehead torsion, simple homotopy. In: Spaces of Homotopy Self-Equivalences. Lecture Notes in Mathematics, vol Author: John W.

Rutter. General Topoloftv and its Applicaticps 7 (g7) _ c~j North-Holland Publishing Company THE INVOLUTION CIN WHITEHEAD TORSION Anthony BAK Fakult f Mathematik, Universitdi Bielefeld, 48 Bielefeld, Germany Received 5 May In this note we show that the involution inn the Whitehead group is trivial rroviding the fundamental group is torsion by: Cite this chapter as: Anderson G.A.

() Whitehead torsion. In: Surgery with Coefficients. Lecture Notes in Mathematics, vol Springer, Berlin, Heidelberg. Introduction to Combinatorial Torsions Book.

II Topological Theory of Torsions.- 5 Basics of algebraic topology.- 6 The Reidemeister-Franz torsion.- 7 The Whitehead torsion.- 8 Simple homotopy Author: Vladimir Turaev. The book is divided into two parts, called Algebra and Topology.

In cient cobordism-theoretic and Whitehead torsion conditions for compact manifolds of dimension 5 to be homeomorphic. Generically, assembly is the passage from a local input to a global output.

This book considers deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and characterizes axiomatically the assumptions under which such results hold.

Included are methods of calculation, numerous calculations, finite generation results, Whitehead torsion and other areas.

Some references are given. The book assumes familiarity with cell complexes, homology and : Springer-Verlag Berlin Heidelberg. $\begingroup$ There was a nice paper by Eckmann and a paper by Larry Siebenmann which gave a purely geometric approach to Whitehead torsion. (I worked out an abstract version of this in my book with Heiner Kamps.) There is sense in which it all comes down to a generalisation of rewriting theory.

structures in homotopy theory, via Whitehead torsion and the Wall niteness and surgery obstructions. In the topological applications the ground ring Ais the group ring Z[ˇ] of the fundamental group -theory a geometric structure is a nite CWcomplex, while for L-theory it is a compact manifold.

The lower K-andL-groups are the obstruc. Life. (Henry) Whitehead was the son of the Right Rev. Henry Whitehead, Bishop of Madras, who had studied mathematics at Oxford, and was the nephew of Alfred North Whitehead and Isobel Duncan.

He was brought up in Oxford, went to Eton and read mathematics at Balliol College, a year working as a stockbroker, at Buckmaster & Moore, he started a PhD in at Princeton Born: 11 NovemberMadras (Chennai), India. Generalizations and functoriality of the torsion.

Homological computation of the torsion --II. Topological Theory of Torsions. Basics of algebraic topology. The Reidemeister-Franz torsion.

The Whitehead torsion. Simple homotopy equivalences. Reidemeister torsions and homotopy equivalences. The torsion of lens spaces. In mathematics, Whitehead torsion is an invariant of an h-cobordism in a Whitehead group, that is important in simple homotopy theory and surgery is named for J.

Whitehead. Whitehead torsion. Suppose that "W" is an h-cobordism from "M" to "N"; this means roughly that "W" is a manifold with boundary the union of "M" and "N" and that "W" is homotopy equivalent to both "M" and "N".

Inoue T. () The equivariant whitehead torsions of equivariant homotopy equivalences between the unit spheres of representations of cyclic groups. In: Kawakubo K.

(eds) Transformation Groups. Lecture Notes in Mathematics, vol Cited by: 1.This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds.

The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C.

Whitehead, J. Milnor and the author.Alfred North Whitehead return to religion-online Alfred North Whitehead by Norman Pittenger Dr.

Pittenger, philosopher and theologian, was a senior member of King’s College, Cambridge for many years, then Professor of Christian Apologetics at the General Theological Seminary in New York City, before retiring in File Size: KB.