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width: 0.3em;"></span> <a href="/nlab/show/HomePage" accesskey="H" title="Home page">Home Page</a> | <a href="/nlab/all_pages" accesskey="A" title="List of all pages">All Pages</a> | <a href="/nlab/latest_revisions" accesskey="U" title="Latest edits and page creations">Latest Revisions</a> | <a href="https://nforum.ncatlab.org/discussion/8426/#Item_3" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</a> | <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>Contents</title></head> <body> <p>This entry colllects material related to the book</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Glen+Bredon">Glen Bredon</a>,</p> <p><strong>Introduction to compact transformation groups</strong></p> <p>Academic Press 1972</p> <p><a href="https://www.elsevier.com/books/introduction-to-compact-transformation-groups/bredon/978-0-12-128850-1">ISBN 9780080873596</a></p> <p><a href="https://jfdmath.sitehost.iu.edu/seminar/Bredon,Introduction_to_Compact_Transformation_Groups.pdf">pdf</a></p> </li> </ul> <p>on <a class="existingWikiWord" href="/nlab/show/transformation+groups">transformation groups</a>/<a class="existingWikiWord" href="/nlab/show/topological+G-spaces">topological G-spaces</a> and their <a class="existingWikiWord" href="/nlab/show/equivariant+differential+topology">equivariant differential topology</a>, <a class="existingWikiWord" href="/nlab/show/equivariant+homotopy+theory">equivariant homotopy theory</a> and <a class="existingWikiWord" href="/nlab/show/equivariant+cohomology">equivariant cohomology</a> (<a class="existingWikiWord" href="/nlab/show/Bredon+cohomology">Bredon cohomology</a>).</p> <p>See also</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Tammo+tom+Dieck">Tammo tom Dieck</a>, <em><a class="existingWikiWord" href="/nlab/show/Transformation+Groups+and+Representation+Theory">Transformation Groups and Representation Theory</a></em>, Lecture Notes in Mathematics 766, Springer 1979 (<a href="https://link.springer.com/book/10.1007/BFb0085965">doi:10.1007/BFb0085965</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Tammo+tom+Dieck">Tammo tom Dieck</a>, <em><a class="existingWikiWord" href="/nlab/show/Transformation+Groups">Transformation Groups</a></em>, de Gruyter 1987 (<a href="https://doi.org/10.1515/9783110858372">doi:10.1515/9783110858372</a>)</p> </li> </ul> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#0_background_on_topological_groups_and_lie_groups'>0 Background on Topological Groups and Lie Groups</a></li> <ul> <li><a href='#1_elementary_properties_of_topological_groups'>1. Elementary properties of topological groups</a></li> <li><a href='#2_the_classical_groups'>2. The classical groups</a></li> <li><a href='#3_integration_on_compact_groups'>3. Integration on compact groups</a></li> <li><a href='#4_characteristic_functions_on_compact_groups'>4. Characteristic functions on compact groups</a></li> <li><a href='#5_lie_groups'>5. Lie groups</a></li> <li><a href='#6_the_structure_of_compact_lie_groups'>6. The structure of compact Lie groups</a></li> </ul> <li><a href='#i_transformation_groups'>I Transformation Groups</a></li> <li><a href='#ii_general_theory_of_spaces'>II General Theory of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>G</mi></mrow><annotation encoding="application/x-tex">G</annotation></semantics></math>-Spaces</a></li> <ul> <li><a href='#1_fiber_bundles'>1. Fiber bundles</a></li> <li><a href='#2_associated_bundles'>2. Associated bundles</a></li> <li><a href='#3_twisted_products_with_a_compact_group'>3. Twisted products with a compact group</a></li> <li><a href='#4_tubes_and_slices'>4. Tubes and slices</a></li> </ul> <li><a href='#iii_homological_theory_of_finite_group_actions'>III Homological Theory of Finite Group Actions</a></li> <li><a href='#iv_locally_smooth_actions_on_manifolds'>IV Locally Smooth Actions on Manifolds</a></li> <li><a href='#v_actions_with_few_orbit_types'>V Actions with Few Orbit Types</a></li> <li><a href='#vi_smooth_actions'>VI Smooth Actions</a></li> <li><a href='#chapter_vii_cohomology_structure_of_fixed_point_sets'>Chapter VII Cohomology Structure of Fixed Point Sets</a></li> </ul> </div> <h2 id="0_background_on_topological_groups_and_lie_groups">0 Background on Topological Groups and Lie Groups</h2> <h3 id="1_elementary_properties_of_topological_groups">1. Elementary properties of topological groups</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+group">topological group</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/normalizer+subgroup">normalizer subgroup</a></p> </li> </ul> <h3 id="2_the_classical_groups">2. The classical groups</h3> <ul> <li><a class="existingWikiWord" href="/nlab/show/classical+Lie+group">classical Lie group</a></li> </ul> <h3 id="3_integration_on_compact_groups">3. Integration on compact groups</h3> <ul> <li><a class="existingWikiWord" href="/nlab/show/Haar+measure">Haar measure</a></li> </ul> <h3 id="4_characteristic_functions_on_compact_groups">4. Characteristic functions on compact groups</h3> <h3 id="5_lie_groups">5. Lie groups</h3> <ul> <li><a class="existingWikiWord" href="/nlab/show/Lie+group">Lie group</a></li> </ul> <h3 id="6_the_structure_of_compact_lie_groups">6. The structure of compact Lie groups</h3> <ul> <li><a class="existingWikiWord" href="/nlab/show/compact+Lie+group">compact Lie group</a></li> </ul> <h2 id="i_transformation_groups">I Transformation Groups</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/group+action">group action</a>, <a class="existingWikiWord" href="/nlab/show/topological+G-space">topological G-space</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/equivariant+function">equivariant function</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/isotropy+group">isotropy group</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/orbit">orbit</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/homogeneous+space">homogeneous space</a>, <a class="existingWikiWord" href="/nlab/show/coset+space">coset space</a>, <a class="existingWikiWord" href="/nlab/show/orbit+type">orbit type</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/slice+theorem">slice theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/fixed+points">fixed points</a></p> </li> </ul> <h2 id="ii_general_theory_of_spaces">II General Theory of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>G</mi></mrow><annotation encoding="application/x-tex">G</annotation></semantics></math>-Spaces</h2> <h3 id="1_fiber_bundles">1. Fiber bundles</h3> <ul> <li><a class="existingWikiWord" href="/nlab/show/fiber+bundle">fiber bundle</a></li> </ul> <h3 id="2_associated_bundles">2. Associated bundles</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/associated+bundle">associated bundle</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/slice+theorem">slice theorem</a></p> </li> </ul> <h3 id="3_twisted_products_with_a_compact_group">3. Twisted products with a compact group</h3> <h3 id="4_tubes_and_slices">4. Tubes and slices</h3> <h2 id="iii_homological_theory_of_finite_group_actions">III Homological Theory of Finite Group Actions</h2> <h2 id="iv_locally_smooth_actions_on_manifolds">IV Locally Smooth Actions on Manifolds</h2> <h2 id="v_actions_with_few_orbit_types">V Actions with Few Orbit Types</h2> <h2 id="vi_smooth_actions">VI Smooth Actions</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/equivariant+tubular+neighbourhood">equivariant tubular neighbourhood</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/invariant+Riemannian+metric">invariant Riemannian metric</a></p> </li> </ul> <h2 id="chapter_vii_cohomology_structure_of_fixed_point_sets">Chapter VII Cohomology Structure of Fixed Point Sets</h2> <div class="property">category: <a class="category_link" href="/nlab/all_pages/reference">reference</a></div></body></html> </div> <div class="revisedby"> <p> Last revised on October 28, 2024 at 15:52:22. 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