By Gunnar Carlsson (auth.), Gunnar E. Carlsson, Ralph L. Cohen, Wu-Chung Hsiang, John D. S. Jones (eds.)

ISBN-10: 1461395267

ISBN-13: 9781461395263

ISBN-10: 1461395283

ISBN-13: 9781461395287

In 1989-90 the Mathematical Sciences examine Institute carried out a application on *Algebraic Topology and its **Applications*. the most components of focus have been homotopy concept, K-theory, and purposes to geometric topology, gauge thought, and moduli areas. Workshops have been performed in those 3 components. This quantity involves invited, expository articles at the themes studied in this software. They describe fresh advances and aspect to attainable new instructions. they need to end up to be beneficial references for researchers in Algebraic Topology and comparable fields, in addition to to graduate students.

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In 1989-90 the Mathematical Sciences examine Institute carried out a software on Algebraic Topology and its purposes. the most parts of focus have been homotopy thought, K-theory, and functions to geometric topology, gauge thought, and moduli areas. Workshops have been performed in those 3 parts.

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**Extra info for Algebraic Topology and Its Applications**

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J. Milgram, The structure of spaces of Toeplitz matrices, Topology (to appear). w. Nahm, The algebmic theory of multimonopoles, Lect. Notes in Physics, Berlin, Heidelberg, New York, vol. 180, Springer Verlag, pp. 456-466. A. Pressley, G. Segal, Loop Groups" Oxford U. Press" Oxford. G. Segal, Configumtion spaces and itemted loop spaces, Invent. Math. 21 (1973), 213-22l. G. Segal, The topology of spaces ofmtionalfunctions, Acta Math. 143 (1979), 39-72. L. Sibner and R. Sibner, Classification of singular Sobolev connections by their holonomy, Comm.

We write Bk for the component corresponding to 0~82. In the literature the integer k is referred to as the charge of the pair (A, ¢). The Yang - Mills - Higgs functional is invariant under the gauge group action and so defines a function U : Bk----+lR for each k E Z. By the definition of U (actually its local relationship with the Yang - Mills functional on the associated time invariant connections on lR4) it is not difficult to see that (A, ¢) E A represents a minimum of U if and only if the associated four - dimensional connection a=A+¢dt is self - dual, or anti - self dual: *FO/ = ±FO/.

L. S Jones, Monopoles, Braid Groups, and the Dirac operator" to appear. L. Cohen and D. Shimamoto, Rational junctions, labelled configurations, and Hilbert schemes, Jour. of Lond. Math. Soc. (to appear) (1991). L. S Jones, and J. Rade, The S1 equivariant homotopy type of instantons on S4, to appear. K. Donaldson, Nahm's equations and the classification of monopoles, Comm. Math. Phys. 100 (1984), 387-407. K. Donaldson, Anti-self-dual Yang Mills connections over complez algebraic surfaces and stable vector bundles, Proc.

### Algebraic Topology and Its Applications by Gunnar Carlsson (auth.), Gunnar E. Carlsson, Ralph L. Cohen, Wu-Chung Hsiang, John D. S. Jones (eds.)

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