Equivariant differential topology in an ominimal expansion of the. Superconnections, thom classes, and equivariant differential forms varghese mathai and daniel quillen received 19 february 1985. Section 3 develops a cobordism theory for gmanifolds. Introduction to differential topology people eth zurich. Glen bredon, introduction to compact transformation groups, academic press 1972. The purpose of this paper is to establish basic properties of equivariant differential.
For r this includes the situation of nash gmanifolds and nash gvector bundles treated in 10,8. Equivariant cohomology, homogeneous spaces and graphs. Equivariant differential cohomology 5 wherethelinealongthetop,theonealongthebottomandthediagonalsareexact. Kawakami topology and its applications 123 2002 323349 the purpose of this paper is to establish basic properties of equivariant differential topology in an ominimal expansion of the. Marja kankaanrinta, equivariant collaring, tubular neighbourhood and gluing theorems for proper lie group actions, algebr. To start with, we want to extend the notion of a differential form to the equivariant setting. Download free ebook of equivariant algebraic topology in pdf format or read online by soren illman published on 1972 by. Wasserman received 21 november 1967 introduction the aim of this paper is to establish the basic propositions of differential topology as presented in milnor 9, for example for gmanifolds where g is a compact lie group. Hirsch, differential topology, graduate texts in mathematics. Cyclic homology equivariant homology these keywords were added by machine and not by the authors. Arthur wasserman, section 3 of equivariant differential topology, topology vol.
Equivariant embedding theorems and topological index maps arxiv. Equivariant differential topology in an ominimal expansion of the field of real numbers article in topology and its applications 1232. We hope that this paper will be of use in further study and understanding of differential topology of smooth gmanifolds. Printed in great britain equivariant differential topology arthur g. Specifically with an eye towards equivariant differential topology such as pontryaginthom construction for equivariant cohomotopy. Cyclic homology and equivariant homology springerlink. The construction of topological index maps for equivariant families. Arthur wasserman, equivariant differential topology, topology vol. Much of the topology of the orbit space is encoded in the equivariant cohomology ring hgm. Wasserman, equivariant differential topology, topology 8 1969, 127150. In 1998, goresky, kottwitz and macpherson provided a new method for computing this ring.
Equivariant collaring, tubular neighbourhood and gluing theorems. These are notes for the lecture course differential geometry ii held by the second author at. The subject of equivariant differential topology is the enhancement of results of differential topology from plain manifoldstopological spaces to. Polack differential topology translated in to persian by m. Pdf on apr 11, 2014, victor william guillemin and others published v. The definition of equivariant differential cohomology. We establish basic properties of differential topology for definable crg. This process is experimental and the keywords may be updated as the learning algorithm improves.