Publication

Cobordism, Cohomology Theories and Formal Group Laws

2011
Student Projects

Abstract

We first explore the notion of G-manifold, cobordism and then discuss the generalized Pontrjagin-Thom Theorem. We then compute the cobordism rings Ω (...) using stable homotopy theory. Secondly, we investigate the relations between cohomology theories and formal group laws. This is the very beginning of the so called chromatic homotopy theory. For any complex oriented cohomology theories, we associate a formal group law. We show that the formal group law associated to complex cobordism is universal. Finally, for a suitable formal group law we give a way to realize it into a generalized homology theory.

Official source

https://infoscience.epfl.ch/entities/publication/07f92772-8386-4b47-a9de-14968cdbb806

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2011
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/07f92772-8386-4b47-a9de-14968cdbb806

About this result

Related concepts (32)

Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.

Cobordism

In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher. The boundary of an (n + 1)-dimensional manifold W is an n-dimensional manifold ∂W that is closed, i.e., with empty boundary.

Homotopy theory

In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topology, the theory has also been used in other areas of mathematics such as algebraic geometry (e.g., A1 homotopy theory) and (specifically the study of ). In homotopy theory and algebraic topology, the word "space" denotes a topological space.

Related publications (3)

Cobordism, Cohomology Theories and Formal Group Laws

Chat with Graph Search

Quantization of the Willmore energy in Riemannian manifolds

Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy

Why H Z-algebra Spectra are Differential Graded Algebras?