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Author: Henryk Toruńczyk
Publisher: American Mathematical Soc.
ISBN: 0821824716
Category : Mathematics
Languages : en
Pages : 85
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Book Description
We analyze fibrations over paracompact Hausdorff bases with locally compact ANR fibers and show that a fibred analog of the first author's characterization of Hilbert cube manifolds detects the Hilbert cube manifold bundles if the fibers are compact or the base is semi-locally contractible. This shows that Hurewicz fibrations with Hilbert cube manifold fibers over CW-complexes with compact fibers or proper fiber transport are bundles.
Author: Henryk Toruńczyk
Publisher: American Mathematical Soc.
ISBN: 0821824716
Category : Mathematics
Languages : en
Pages : 85
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Book Description
We analyze fibrations over paracompact Hausdorff bases with locally compact ANR fibers and show that a fibred analog of the first author's characterization of Hilbert cube manifolds detects the Hilbert cube manifold bundles if the fibers are compact or the base is semi-locally contractible. This shows that Hurewicz fibrations with Hilbert cube manifold fibers over CW-complexes with compact fibers or proper fiber transport are bundles.
Author: Bruce Hughes
Publisher: American Mathematical Soc.
ISBN: 0821820699
Category : Mathematics
Languages : en
Pages : 113
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Book Description
This work formulates and proves a geometric version of the fundamental theorem of algebraic K-theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a finite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric version of the fundamental theorem of lower algebraic K-theory. The main new innovation is a geometrically defined nil space.
Author: R.B. Sher
Publisher: Elsevier
ISBN: 0080532853
Category : Mathematics
Languages : en
Pages : 1145
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Book Description
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 912
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Book Description
Author: Dai Tamaki
Publisher: World Scientific
ISBN: 9811238103
Category : Mathematics
Languages : en
Pages : 337
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Book Description
This book is an introduction to fiber bundles and fibrations. But the ultimate goal is to make the reader feel comfortable with basic ideas in homotopy theory. The author found that the classification of principal fiber bundles is an ideal motivation for this purpose. The notion of homotopy appears naturally in the classification. Basic tools in homotopy theory such as homotopy groups and their long exact sequence need to be introduced. Furthermore, the notion of fibrations, which is one of three important classes of maps in homotopy theory, can be obtained by extracting the most essential properties of fiber bundles. The book begins with elementary examples and then gradually introduces abstract definitions when necessary. The reader is assumed to be familiar with point-set topology, but it is the only requirement for this book.
Author: Steven Zelditch
Publisher: American Mathematical Soc.
ISBN: 0821825267
Category : Curves on surfaces
Languages : en
Pages : 113
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Book Description
This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The second problem is to determine the distribution of eigenfunctions (in microlocal sense) in the unit tangent bundle.
Author: Shari A. Prevost
Publisher: American Mathematical Soc.
ISBN: 0821825275
Category : Mathematics
Languages : en
Pages : 113
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Book Description
We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.
Author: Bruce Arie Reznick
Publisher: American Mathematical Soc.
ISBN: 0821825232
Category : Mathematics
Languages : en
Pages : 169
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Book Description
This work initiates a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms and the resulting implications in real algebraic geometry, number theory, combinatorics, functional analysis, and numerical analysis. The proofs utilize elementary techniques from linear algebra, convexity, number theory, and real algebraic geometry and many explicit examples and relevant historical remarks are presented.
Author: John David Fay
Publisher: American Mathematical Soc.
ISBN: 082182550X
Category : Mathematics
Languages : en
Pages : 137
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Book Description
This memoir is a study of Ray-Singer analytic torsion for hermitian vector bundles on a compact Riemann surface [italic]C. The torsion is expressed through the trace of a modified resolvent. Thus, one can develop perturbation-curvature formulae for the Green-Szegö kernel and also for the torsion in terms of the Ahlfors-Bers complex structure of the Teichmuller space and Mumford complex structure of the moduli space of stable bundles of degree zero on [italic]C.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 836
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Book Description
