§ 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.