The construction of topological index maps for equivariant families. The subject of equivariant differential topology is the enhancement of results of differential topology from plain manifoldstopological spaces to. 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. Download free ebook of equivariant algebraic topology in pdf format or read online by soren illman published on 1972 by. Equivariant differential cohomology 5 wherethelinealongthetop,theonealongthebottomandthediagonalsareexact.
Marja kankaanrinta, equivariant collaring, tubular neighbourhood and gluing theorems for proper lie group actions, algebr. Equivariant differential topology university of rochester mathematics. Introduction to differential topology people eth zurich. Cyclic homology and equivariant homology springerlink. We hope that this paper will be of use in further study and understanding of differential topology of smooth gmanifolds. Much of the topology of the orbit space is encoded in the equivariant cohomology ring hgm. We establish basic properties of differential topology for definable crg. Arthur wasserman, equivariant differential topology, topology vol. Discussion in the context of global equivariant homotopy theory is in.
Glen bredon, introduction to compact transformation groups, academic press 1972. Polack differential topology translated in to persian by m. Wasserman, equivariant differential topology, topology 8 1969, 127150. To start with, we want to extend the notion of a differential form to the equivariant setting. This process is experimental and the keywords may be updated as the learning algorithm improves.
Section 3 develops a cobordism theory for gmanifolds. Atiyah l has proved a similar theorem for compact topological spaces. Printed in great britain equivariant differential topology arthur g. Equivariant embedding theorems and topological index maps arxiv. Specifically with an eye towards equivariant differential topology such as pontryaginthom construction for equivariant cohomotopy. 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. Equivariant differential topology in an ominimal expansion of the field of real numbers article in topology and its applications 1232. Hirsch, differential topology, graduate texts in mathematics. In 1998, goresky, kottwitz and macpherson provided a new method for computing this ring. Equivariant collaring, tubular neighbourhood and gluing theorems. Equivariant cohomology, homogeneous spaces and graphs. These are notes for the lecture course differential geometry ii held by the second author at. The definition of equivariant differential cohomology. Arthur wasserman, section 3 of equivariant differential topology, topology vol.734 954 986 1134 1021 366 764 1202 1028 814 330 1505 1193 476 1173 699 1442 1200 1259 1382 58 347 428 250 711 293 420 1180 362 1141 1105 1126 1450 903 1077 620 1036 594 1183 857 443 769 526 1347 1393