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Charles Matthews
Charles Matthews
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Can I be the first to recommend Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 1971 29–56 (1971).

From the MR review: "In this important and elegant paper the author gives new elementary proofs of the structure theorems for the unoriented cobordism ring $N^\ast$ and the complex cobordism ring $U^\ast$, together with new results and methods. Everyone working in cobordism theory should read this paper."

The paper was revolutionary in (at least) two ways.

  1. The proofs are almost entirely geometric, with cobordism classes represented by proper oriented maps of manifolds. Quillen cites Grothendieck as inspiration for this, and such methods should appeal to algebraic geometers familiar with the Chow ring.
  2. Formal group methods are used to prove results in stable homotopy theory. It's hard to underestimateoverestimate the impact this has had. Indeed almost all of the modern connections between homotopy theory and algebraic geometry seem to go through formal groups, drawing influence from Quillen's idea.

Can I be the first to recommend Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 1971 29–56 (1971).

From the MR review: "In this important and elegant paper the author gives new elementary proofs of the structure theorems for the unoriented cobordism ring $N^\ast$ and the complex cobordism ring $U^\ast$, together with new results and methods. Everyone working in cobordism theory should read this paper."

The paper was revolutionary in (at least) two ways.

  1. The proofs are almost entirely geometric, with cobordism classes represented by proper oriented maps of manifolds. Quillen cites Grothendieck as inspiration for this, and such methods should appeal to algebraic geometers familiar with the Chow ring.
  2. Formal group methods are used to prove results in stable homotopy theory. It's hard to underestimate the impact this has had. Indeed almost all of the modern connections between homotopy theory and algebraic geometry seem to go through formal groups, drawing influence from Quillen's idea.

Can I be the first to recommend Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 1971 29–56 (1971).

From the MR review: "In this important and elegant paper the author gives new elementary proofs of the structure theorems for the unoriented cobordism ring $N^\ast$ and the complex cobordism ring $U^\ast$, together with new results and methods. Everyone working in cobordism theory should read this paper."

The paper was revolutionary in (at least) two ways.

  1. The proofs are almost entirely geometric, with cobordism classes represented by proper oriented maps of manifolds. Quillen cites Grothendieck as inspiration for this, and such methods should appeal to algebraic geometers familiar with the Chow ring.
  2. Formal group methods are used to prove results in stable homotopy theory. It's hard to overestimate the impact this has had. Indeed almost all of the modern connections between homotopy theory and algebraic geometry seem to go through formal groups, drawing influence from Quillen's idea.
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Mark Grant
Mark Grant
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Can I be the first to recommend Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 1971 29–56 (1971).

From the MR review: "In this important and elegant paper the author gives new elementary proofs of the structure theorems for the unoriented cobordism ring $N^\ast$ and the complex cobordism ring $U^\ast$, together with new results and methods. Everyone working in cobordism theory should read this paper."

The paper was revolutionary in (at least) two ways.

  1. The proofs are almost entirely geometric, with cobordism classes represented by proper oriented maps of manifolds. Quillen cites Grothendieck as inspiration for this, and such methods should appeal to algebraic geometers familiar with the Chow ring.
  2. Formal group methods are used to prove results in stable homotopy theory. It's hard to underestimate the impact this has had. Indeed almost all of the modern connections between homotopy theory and algebraic geometry seem to go through formal groups, drawing influence from Quillen's idea.