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1. CAT'05
Conference on algebraic topology June 27 July 1, 2005 Kraków (Cracow, Poland) . Previous quadrennial Conferences on algebraic topology
http://www.mimuw.edu.pl/~cat05/

2. Differential Forms In Algebraic Topology - Algebraic Topology Journals, Books &
Differential Forms in algebraic topology Geometry Topology. Developed from a first-year graduate course in algebraic topology, this text is an informal
http://www.springer.com/west/home/math/geometry?SGWID=4-10046-22-1256743-0

3. Dror Bar-Natan:Classes:2001-02:Algebraic Topology
Allen Hatcher s algebraic topology (free download; a paper copy is March 12, 14, Class notes for March 12th (the basic idea of algebraic topology,
http://www.math.toronto.edu/~drorbn/classes/0102/AlgTop/index.html

Extractions: Dror Bar-Natan Classes Instructor: Dror Bar-Natan drorbn@math.huji.ac.il Classes: Tuesdays 12:00-14:00 at Mathematics 110 and Thursdays 12:00-14:00 at Sprintzak 213. Review sessions: Thursdays 14:00-15:00 with Boris Chorny chorny@math.huji.ac.il Office hours: Tuesdays 14:00-15:00 in my office, Mathematics 309. Agenda: Learn how algebra and topology interact in the field of Algebraic Topology. Syllabus: Prerequisites: Point set topology and some basic notions of algebra - groups, rings, etc. Reading material: (each student must have a copy) Weekly Material: (Also use the primitive Class Notes Browser March 12, 14 Class notes for March 12th (the basic idea of algebraic topology, Brouwer's theorem, the fundamental group, the fundamental group of the circle).

4. Algebraic Topology
Math reference, an introduction to algebraic topology.
http://www.mathreference.com/at,intro.html

Extractions: Algebraic Topology, An Introduction Introduction As the name suggests, algebraic topology is a marriage of algebra and topology. These branches of mathematics seem unrelated, yet they can be connected in several ways. For instance, a topological space S might be assigned a group G, based on the propertyies of S, in such a way that any space homeomorphic to S will be given the same group G. Therefore, two spaces that exhibit different groups cannot be homeomorphic. Proving a negative is always difficult; this is often the only way we can prove two spaces are different from each other. Consider a simple example, the line and the plane. These spaces seem different enough, yet they have the same cardinality. There are invertible functions that map the plane onto the line and back again. Perhaps one of these functions preserves open sets. Perhaps one dimension is really the same as two, when viewed from the right perspective. This isn't true of course; the plane is different from the line. But we need algebraic topology to prove it. The groups associated with these spaces (actually their compactifications) are different, and that closes the case. The first group that we will assign to a space S is its homotopy group, but before we can do that we need to know what a homotopy is.

5. Groupoids And Crossed Objects In Algebraic Topology
Groupoids and crossed objects in algebraic topology. Ronald Brown. This is an introductory survey of the passage from groups to groupoids and their higher
http://www.intlpress.com/hha/v1/n1/a1/

Extractions: This is an introductory survey of the passage from groups to groupoids and their higher dimensional versions, with most emphasis on calculations with crossed modules and the construction and use of homotopy double groupoids. Homology, Homotopy and Applications, Vol. 1, 1999, No. 1, pp 1-78 Available as: dvi dvi.gz ps ps.gz

6. CONTEMPORARY TRENDS IN ALGEBRAIC GEOMETRY AND ALGEBRAIC TOPOLOGY
CONTEMPORARY TRENDS IN ALGEBRAIC GEOMETRY AND algebraic topology.
http://www.worldscibooks.com/mathematics/4966.html

Extractions: About the Editors Professor S S Chern retired from UC Berkeley and is now based in the Nankai Institute of Mathematics, which he founded in 1985. He is also the founding director of the Mathematical Science Research Institute, Berkeley (1981). He was awarded the National Science Medal in 1975 and Wolf Prize in Mathematics in 1983/4. His area of research was differential geometry where he studied the (now named) Chern characteristic classes in fibre spaces. The Chern Visiting Professorship, begun in 1996, honors the Berkeley professor emeritus widely regarded as the greatest geometer of his generation. "Chern's belief in young people and his encouragement of them had a lot to do with the spectacular growth of geometry in the second half of this century" mathematician Blaine Lawson has said. "It is not easy to find a geometer who was not for some period of time either a student or a post-doctoral fellow in the orbit of Chern. (http://math.berkeley.edu/) Professor Chern is also the editor of the book  Selected Papers of Wei-Liang Chow , also published by World Scientific Publishing.

7. Algebraic And Geometric Topology
Interests algebraic topology and its applications, TQFT s and CFT, noncommutative geometry, operads and higher dimensional categories, mapping

8. Algebraic Topology
algebraic topology is the study of topological spaces using tools of an algebraic nature, such as homology groups, cohomology groups and homotopy groups.
http://jdc.math.uwo.ca/algtop/

Extractions: Algebraic topology is the study of topological spaces using tools of an algebraic nature, such as homology groups, cohomology groups and homotopy groups. It is one of the major accomplishments of twentieth century mathematics and has applications to many areas of mathematics and to other fields, such as physics, computer science, and economics. I encourage students from other departments to attend. This is a first course in algebraic topology which will introduce the invariants mentioned above, explain their basic properties and develop both methods of computation and geometric intuition. Course outline: Instructor: Dan Christensen E-mail: jdc@uwo.ca Office: Middlesex 103b. Office Phone: Office Hours: to be determined. Class times and location: Mondays, 11 am to 12:20 pm, and Fridays, 1:30 pm to 2:50 pm. MC107. Prerequisites: Algebra I (group theory, Math 302a) and General Topology (Math 404a); or permission of instructor. (Students from other departments are welcome and should consult with me.) Web page: This page is available at http://jdc.math.uwo.ca/algtop

9. Foundations Of Algebraic Topology
Both Point Set Topology and algebraic topology attempt to describe and analyze the properties of geometric objects which are invariant under continuous
http://www.sjsu.edu/faculty/watkins/algtop.htm

Extractions: USA Foundations of Algebraic Topology Both Point Set Topology and Algebraic Topology attempt to describe and analyze the properties of geometric objects which are invariant under continuous mappings. Algebraic Topology does this using an indirect approach. Each geometric object is associated with a set of algebraic structures, usually groups . Questions about the geometric objects are converted into questions about the associated groups. This strategy is analogous to the way transform methods are used to solve differential equations. Laplace and Fourier transforms are used to convert a differential equation into a strictly algebraic equation. Algebraic methods are used to solve for the transform of the solution to the differential equation. The inverse transform is applied to the transform of the solution to get the solution to the differential equation. n Let X be a sphere in 3-space and let Y be a torus also in 3-space. The groups to be constructed are based upon loops that begin and end at some point P outside of X and Y. A loop is just a directed path in which the the beginning point and the end point are the same point. Two loops, x and x , can be added by attaching the beginning part of the second loop to the ending part of the first loop. There is also a zero loop, one that does not leave the point P. The situation is illustrated in the diagram below.

10. Research In Algebraic Topology
Geometry and algebraic topology play major roles throughout Mathematics and its applications, with geometric and topological ideas often being indispensable
http://www.maths.gla.ac.uk/research/groups/algebraic_topology/

Extractions: Text only Department of Mathematics Home Research > Algebraic Topology Home Research Algebra Algebraic Topology ... Contact Algebraic Topology Geometry and Algebraic Topology play major roles throughout Mathematics and its applications, with geometric and topological ideas often being indispensable. situations than other Geometers.There have also been significant interactions with many areas of Algebra, and indeed much of Algebraic Topology can be viewed as `applied algebra' as well as being a major source of innovative algebraic ideas. In the words of Hermann Weyl: ` In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics Departmental research activity in Topology occurs in the following areas. Dr A.J. Baker

11. CAT04 - Arolla Conference On Algebrac Topology
CAT04. Arolla Conference on algebraic topology. August 24 through 29, 2004. Welcome to the main page of the CAT04 web site !
http://www2.unil.ch/cat04/

12. Short Course On Algebraic Topology, Gliwice, Poland, 3.9.2007
This (very) short course on algebraic topology shall give an introduction to some essenetial concepts of this field of mathematics the fundamental group
http://www.mathstat.helsinki.fi/~fluch/at_gliwice-07/

Extractions: Departmental front page News ... People In English (Gliwice, Poland, 3.9.2007) Martin Fluch This (very) short course on Algebraic Topology shall give an introduction to some essenetial concepts of this field of mathematics: the fundamental group and homology theories. As an example we will show how those results are used to prove that the Euclidean spaces R n and R m are not homeomorphic if n is not equal to m , which is not possible to prove in a purely topological way. This short lecture will be part of the 3rd Summer School of Algebra and Topology which is held in Gliwice , Poland from 3rd to 7th of September. The notes to the lecture can be downloaded here: alg_top_intro.pdf Fred Croom. Basic Concepts of Algebraic Topology . Undergraduate Texts in Mathematics. Springer-Verlag, 1978. Glen Bredon. Topology and Geometry . Graduate texts in mathematics. Springer-Verlag, 1993. Jean Dieudonne

13. FreeScience - Books - Algebraic Topology
This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in
http://www.freescience.info/books.php?id=102

14. Universität Osnabrück - Institut Für Mathematik - Conference On Algebraic Top
mailtoJP. Conference on algebraic topology. Osnabrück (Germany) Triangulated categories are fundamental tools in both algebra and topology.
http://www.mathematik.uni-osnabrueck.de/topRainer65.html

Extractions: We outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed simplicial groups and the homological algebra of module-valued functors. The symmetric homology of group algebras is related to stable homotopy theory. Two spectral sequences for computing symmetric homology are constructed. The relation to cyclic homology is discussed and a couple of conjectures towards further work are proposed. Clemens Berger (Nizza) The lattice path operad

15. Mathematics :: Algebraic Topology --  Britannica Online Encyclopedia
Britannica online encyclopedia article on mathematics, algebraic topology The early 20th century saw the emergence of a number of theories whose power and
http://www.britannica.com/eb/article-66032/mathematics

Extractions: Table of Contents Expand all Collapse all Introduction Ancient mathematical sources ... Assessment of Egyptian mathematics Greek mathematics The development of pure mathematics The pre-Euclidean period The Elements The three classical problems Geometry in the 3rd century ... Applied geometry Later trends in geometry and arithmetic Greek trigonometry and mensuration Number theory Survival and influence of Greek mathematics Origins ... The Renaissance Mathematics in the 17th and 18th centuries The 17th century Institutional background Numerical calculation Analytic geometry ... Newton and Leibniz The 18th century Institutional background Analysis and mechanics History of analysis Other developments ... Mathematical physics Algebraic topology Developments in pure mathematics Mathematical physics and the theory of groups Additional Reading General sources Mathematics in ancient Mesopotamia Mathematics in ancient Egypt Greek mathematics ... Print this Table of Contents Linked Articles manifolds Enrico Betti Emmy Noether homology ... Fields Medal Shopping

The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications

17. Algebraic Topology
Superb 1year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.
http://store.doverpublications.com/0486691314.html

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18. Algebraic Topology
algebraic topology. Complex Analysis and Riemann Surfaces algebraic topology I I Homology Theory. Singular homology definition, simple computations