Bioperads and hopf bialgebras in cobordism theory

1999 ◽  
Vol 65 (2) ◽  
pp. 221-229 ◽  
Author(s):  
V. A. Smirnov
Keyword(s):  
Cobordism Theory

A survey of bordism and cobordism

1986 ◽  
Vol 100 (2) ◽  
pp. 207-223 ◽  
Author(s):  
Peter S. Landweber
Keyword(s):  
Present Article ◽  
Cobordism Theory

In the paper ‘Bordism and Cobordism’, which appeared in vol. 57 (1961) of this journal [5], Michael Atiyah introduced and began the study of bordism and cobordism theory. The present article will trace developments in this area since this beginning.

Quillen's work on formal group laws and complex cobordism theory

2013 ◽  
Vol 11 (3) ◽  
pp. 493-506
Author(s):  
Douglas C. Ravenel
Keyword(s):  
Algebraic Topology ◽  
Formal Group ◽  
Home Page ◽  
Complex Cobordism ◽  
Cobordism Theory ◽  
Formal Group Laws

AbstractIn 1969 Quillen discovered a deep connection between complex cobordism and formal group laws which he announced in [Qui69]. Algebraic topology has never been the same since. We will describe the content of [Qui69] and then discuss its impact on the field. This paper is a writeup of a talk on the same topic given at the Quillen Conference at MIT in October 2012. Slides for that talk are available on the author's home page.

scholarly journals Manifolds of positive scalar curvature and conformal cobordism theory

2002 ◽  
Vol 324 (4) ◽  
pp. 817-840 ◽  
Author(s):  
K. Akutagawa ◽  
B. Botvinnik ◽  
Not Available Not Available
Keyword(s):  
Scalar Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Cobordism Theory

Variations on a theme of rationality of cycles

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Nikita Karpenko
Keyword(s):  
Function Field ◽  
Algebraic Cycles ◽  
Base Field ◽  
Arbitrary Characteristic ◽  
Steenrod Operations ◽  
Cobordism Theory ◽  
Characteristic 2 ◽  
Algebraic Cobordism ◽  
Variations On A Theme

AbstractWe prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular, Vishik’s construction of fields of u-invariant 2r + 1, for r ≥ 3, is extended to arbitrary characteristic ≠ 2.

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