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Here is the reference trail, according to this source:

Borel made the key observation [1] that the cohomology of the fixed point set was closely related to a torsion-free quotient. In the 1960’s, this was formalized as the “localization theorem” of Borel-Atiyah-Segal-Quillen [2,3].

1. A. Borel, Seminar on transformation groups, Annals of Math. Studies 46, Princeton (1960) [Sect. XII Theorem 3.4]

2. M.F. Atiyah and G. Segal, Equivariant cohomology and localization, lecture notes, 1965, Warwick.

3. D. Quillen, The Spectrum of an Equivariant Cohomology Ring I, Annals of Mathematics 94, 549–572 (1971). [Theorem 4.4].

A more extensive overview of the literature leading up to, and following after this localization theorem can be found here (section 1.7). In addition to the unpublished 1965 lecture notes of Atiyah and Segal, there is a 1968 publication [4], crediting the theorem to Segal [5].

4. M.F. Atiyah and G.B Segal: Index of elliptic operators II, Ann. Math. 87, 531–545 (1968).

5. G.B. Segal, Equivariant K-theory, Publ. Math. Inst. Hautes Etudes (Paris) 34, 129-151 (1968).

Here is the reference trail, according to this source:

Borel made the key observation [1] that the cohomology of the fixed point set was closely related to a torsion-free quotient. In the 1960’s, this was formalized as the “localization theorem” of Borel-Atiyah-Segal-Quillen [2,3].

1. A. Borel, Seminar on transformation groups, Annals of Math. Studies 46, Princeton (1960) [Sect. XII Theorem 3.4]

2. M.F. Atiyah and G. Segal, Equivariant cohomology and localization, lecture notes, 1965, Warwick.

3. D. Quillen, The Spectrum of an Equivariant Cohomology Ring I, Annals of Mathematics 94, 549–572 (1971). [Theorem 4.4].

A more extensive overview of the literature leading up to, and following after the localization theorem can be found here (section 1.7). In addition to the unpublished 1965 lecture notes of Atiyah and Segal, there is a 1968 publication [4], crediting the theorem to Segal [5] (who writes that "The theory was invented by Professor Atiyah, and most of the results are due to him.").

4. M.F. Atiyah and G.B Segal: Index of elliptic operators II, Ann. Math. 87, 531–545 (1968).

5. G.B. Segal, Equivariant K-theory, Publ. Math. Inst. Hautes Etudes (Paris) 34, 129-151 (1968).

Here is the reference trail, according to this source:

Borel made the key observation [1] that the cohomology of the fixed point set was closely related to a torsion-free quotient. In the 1960’s, this was formalized as the “localization theorem” of Borel-Atiyah-Segal-Quillen [2,3].

1. A. Borel, Seminar on transformation groups, Annals of Math. Studies 46, Princeton (1960).

2. M.F. Atiyah and G. Segal, Equivariant cohomology and localization, lecture notes, 1965, Warwick.

3. D. Quillen, The Spectrum of an Equivariant Cohomology Ring I, Annals of Mathematics 94, 549–572 (1971). [Theorem 4.4].

A more extensive overview of the literature leading up to, and following after this localization theorem can be found here (section 1.7). In addition to the unpublished 1965 lecture notes of Atiyah and Segal, there is a 1968 publication [4], crediting the theorem to a publication of Segal [5].

4. M.F. Atiyah and G.B Segal: Index of elliptic operators II, Ann. Math. 87, 531–545 (1968).

5. G.B. Segal, Equivariant K-theory, Publ. Math. Inst. Hautes Etudes (Paris) 34, 129-151 (1968).

Here is the reference trail, according to this source:

Borel made the key observation [1] that the cohomology of the fixed point set was closely related to a torsion-free quotient. In the 1960’s, this was formalized as the “localization theorem” of Borel-Atiyah-Segal-Quillen [2,3].

1. A. Borel, Seminar on transformation groups, Annals of Math. Studies 46, Princeton (1960) [Sect. XII Theorem 3.4]

2. M.F. Atiyah and G. Segal, Equivariant cohomology and localization, lecture notes, 1965, Warwick.

3. D. Quillen, The Spectrum of an Equivariant Cohomology Ring I, Annals of Mathematics 94, 549–572 (1971). [Theorem 4.4].

A more extensive overview of the literature leading up to, and following after this localization theorem can be found here (section 1.7). In addition to the unpublished 1965 lecture notes of Atiyah and Segal, there is a 1968 publication [4], crediting the theorem to Segal [5].

4. M.F. Atiyah and G.B Segal: Index of elliptic operators II, Ann. Math. 87, 531–545 (1968).

5. G.B. Segal, Equivariant K-theory, Publ. Math. Inst. Hautes Etudes (Paris) 34, 129-151 (1968).

Here is the reference trail, according to this source:

Borel made the key observation [1] that the cohomology of the fixed point set was closely related to a torsion-free quotient. In the 1960’s, this was formalized as the “localization theorem” of Borel-Atiyah-Segal-Quillen [2,3].

1. A. Borel, Seminar on transformation groups, Annals of Math. Studies 46, Princeton (1960).

2. M.F. Atiyah and G. Segal, Equivariant cohomology and localization, lecture notes, 1965, Warwick.

3. D. Quillen, The Spectrum of an Equivariant Cohomology Ring I, Annals of Mathematics 94, 549–572 (1971). [Theorem 4.4].

A more extensive overview of the literature leading up to, and following after this localization theorem can be found here (section 1.7). In addition to the unpublished 1965 lecture notes of Atiyah and Segal, there is a 1968 publication:

M.F. Atiyah, G. Segal: Index of elliptic operators II, Ann. Math. 87, 531–545 (1968).

Here is the reference trail, according to this source:

Borel made the key observation [1] that the cohomology of the fixed point set was closely related to a torsion-free quotient. In the 1960’s, this was formalized as the “localization theorem” of Borel-Atiyah-Segal-Quillen [2,3].

1. A. Borel, Seminar on transformation groups, Annals of Math. Studies 46, Princeton (1960).

2. M.F. Atiyah and G. Segal, Equivariant cohomology and localization, lecture notes, 1965, Warwick.

3. D. Quillen, The Spectrum of an Equivariant Cohomology Ring I, Annals of Mathematics 94, 549–572 (1971). [Theorem 4.4].

A more extensive overview of the literature leading up to, and following after this localization theorem can be found here (section 1.7). In addition to the unpublished 1965 lecture notes of Atiyah and Segal, there is a 1968 publication [4], crediting the theorem to a publication of Segal [5].

4. M.F. Atiyah and G.B Segal: Index of elliptic operators II, Ann. Math. 87, 531–545 (1968).

5. G.B. Segal, Equivariant K-theory, Publ. Math. Inst. Hautes Etudes (Paris) 34, 129-151 (1968).