Applications of operads to homotopy theory and homological algebra

Project Information

Grant agreement ID: FMBI982967

Start date

End date

Funded under

• Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998

Total cost No data

EU contribution No data

Coordinated by

MAX-PLANCK-GESELLSCHAFT ZUR FOERDERUNG DER WISSENSCHAFTEN E.V.
Germany

Objective

Research objectives and content
This project is concerned with the following applications of operads: The unstable Adams spectral sequence is the main tool for calculating the homotopy type of a topological space. One version of this spectral sequence is based on a model of the loop space construction. Another spectral sequence in homotopy theory based on the loop space construction is Barratt's desuspension spectral sequence. I propose myself to improve these calculational tools by generalizing the construction of these spectral sequences to iterated loop spaces. The little $r$-cubes operad encodes the structure of an $r$-fold loop space and provides an efficient model for this generalization.
Operads theory furnishes a nice homology theory for Poisson algebras. I expect to show that this homology theory determines the cyclic homology of some filtered algebras, generalizing to the non smooth case a method due to Brylinsky.
Training content (objective, benefit and expected impact)
I need knowledge in combinatorial homotopy theory which I may learn from Professor Baues. Moreover, fruitful applications of operads in low dimensional topology, and geometrical physics have been found recently. At the Max Planck Institut, I could establish fruitful international contacts with mathematicians working on these aspects of operads theory. Links with industry / industrial relevance (22)

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.

• natural sciences › mathematics › pure mathematics › algebra
• natural sciences › mathematics › pure mathematics › topology › algebraic topology

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Programme(s)

• FP4-TMR - Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998

Topic(s)

• 0302 - Post-doctoral research training grants

Call for proposal

Data not available

Funding Scheme

RGI - Research grants (individual fellowships)

Coordinator

MAX-PLANCK-GESELLSCHAFT ZUR FOERDERUNG DER WISSENSCHAFTEN E.V.

• EU contribution: No data
• Address: Vivatsgasse 7 ; 53072 BONN ; Germany
• Total cost: No data