By Stefan Jackowski, Bob Oliver, Krzysztof Pawalowski

As a part of the medical task in reference to the seventieth birthday of the Adam Mickiewicz college in Poznan, a global convention on algebraic topology used to be held. within the ensuing complaints quantity, the emphasis is on giant survey papers, a few awarded on the convention, a few written therefore.

**Read or Download Algebraic Topology, Poznan 1989 PDF**

**Best topology books**

Whitehead G. W. Homotopy concept (MIT, 1966)(ISBN 0262230194)(1s)_MDat_

**The Hypoelliptic Laplacian and Ray-Singer Metrics**

This e-book offers the analytic foundations to the speculation of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator performing on the cotangent package deal of a compact manifold, is meant to interpolate among the classical Laplacian and the geodesic move. Jean-Michel Bismut and Gilles Lebeau identify the elemental useful analytic homes of this operator, that's additionally studied from the point of view of neighborhood index idea and analytic torsion.

This publication provides the 1st steps of a conception of confoliations designed to hyperlink geometry and topology of three-d touch buildings with the geometry and topology of codimension-one foliations on 3-dimensional manifolds. constructing virtually independently, those theories at the beginning look belonged to 2 diverse worlds: the speculation of foliations is a part of topology and dynamical structures, whereas touch geometry is the odd-dimensional 'brother' of symplectic geometry.

- Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology
- Fixed Points Degree in NonLinear Analysis
- General topology
- Topological Geometry, Second edition
- Retarded Dynamical Systems: Stability and Characteristic Functions

**Additional info for Algebraic Topology, Poznan 1989**

**Example text**

Any two disks on the plane are homeomorphic; a disk is homeomorphic to the inside of a square or triangle - the corresponding homeomorphisms are easy to construct directly. An interval (a;'b)- = {x E [J;£: a < x < b} on the real line [J;£ is homeomorphic to [J;£. From this it is evident that boundedness of a set and or its diameter are not topological invariants. This is not surprising: boundedness and diameter are definied in terms of a metric, and not in terms of a collection of open sets. A circle is not homeomorphic to a segment [a, b] = {x E [J;£: a ~ x ~ b} because any continuous map of a segment of itself has a fixed point, while a rotation of a circle through 90° about its center has no fixed point.

The map case qJ is a condensation). qJ is continuous if and only if f is continuous (in which Proposition 17. The map f is a quotient map if and only if qJ is a homeomorphism. In other words a quotient map can be characterized as a map whose image is canonically homeomorphic to the decomposition space it generates. Propositions 15 and 17 justify using the term "quotient space" to refer to a decomposition space of a topological space (and not just to the image of a topological space under a quotient map).

In order to address questions like Problems 1-5, it is important to have as wide as possible a spectrum of topological properties preserved by open (closed) maps. It is easy to show that the image under a continuous open map of a space satisfying the first axiom of countability is again a space satisfying the first axiom of countability. Open maps carry spaces with a countable base to spaces with a countable base. Proposition 7. If X is a Frechet-Uryson space and f: X --+ Y isa continuous closed map with f(X) = Y, then Y is also a Frechet-Uryson space.