Ebook: Algebraic Topology and Its Applications

In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces. Workshops were conducted in these three areas. This volume consists of invited, expository articles on the topics studied during this program. They describe recent advances and point to possible new directions. They should prove to be useful references for researchers in Algebraic Topology and related fields, as well as to graduate students.

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In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces. Workshops were conducted in these three areas. This volume consists of invited, expository articles on the topics studied during this program. They describe recent advances and point to possible new directions. They should prove to be useful references for researchers in Algebraic Topology and related fields, as well as to graduate students.

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In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces. Workshops were conducted in these three areas. This volume consists of invited, expository articles on the topics studied during this program. They describe recent advances and point to possible new directions. They should prove to be useful references for researchers in Algebraic Topology and related fields, as well as to graduate students.
Content:
Front Matter....Pages i-vii
Proper Homotopy Theory and Transfers for Infinite Groups....Pages 1-14
The Homotopy Type of Gauge Theoretic Moduli Spaces....Pages 15-55
A Survey of Bounded Surgery Theory and Applications....Pages 57-80
Homotopy Theory of Classifying Spaces of Compact Lie Groups....Pages 81-123
Morita Equivalence, GL n (F q )-Modules, and the Steenrod Algebra....Pages 125-131
Segal’s Burnside Ring Conjecture for Compact Lie Groups....Pages 133-161
On the Lichtenbaum-Quillen Conjectures from a Stable Homotopy-Theoretic Viewpoint....Pages 163-240
Manifolds of Positive Scalar Curvature....Pages 241-267
Back Matter....Pages 269-269

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In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces. Workshops were conducted in these three areas. This volume consists of invited, expository articles on the topics studied during this program. They describe recent advances and point to possible new directions. They should prove to be useful references for researchers in Algebraic Topology and related fields, as well as to graduate students.
Content:
Front Matter....Pages i-vii
Proper Homotopy Theory and Transfers for Infinite Groups....Pages 1-14
The Homotopy Type of Gauge Theoretic Moduli Spaces....Pages 15-55
A Survey of Bounded Surgery Theory and Applications....Pages 57-80
Homotopy Theory of Classifying Spaces of Compact Lie Groups....Pages 81-123
Morita Equivalence, GL n (F q )-Modules, and the Steenrod Algebra....Pages 125-131
Segal’s Burnside Ring Conjecture for Compact Lie Groups....Pages 133-161
On the Lichtenbaum-Quillen Conjectures from a Stable Homotopy-Theoretic Viewpoint....Pages 163-240
Manifolds of Positive Scalar Curvature....Pages 241-267
Back Matter....Pages 269-269
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