Objective
This research proposal is in mathematics, its content is part of algebraic topology and homotopy theory. It aims at deepening our understanding of the homotopy theory of cosimplicial unstable (co-)algebras over the Steenrod algebra and its relation to the homotopy theory of cosimplicial spaces. This is achieved by new methods developed recently by the ER (Dr. Biedermann) and coauthors and by methods from Goodwillie calculus. Specifically, there are three closely related parts/work packages:
1. Prove a general vanishing theorem of higher obstructions for realizing a map on homology as a map of spaces. The theorem is known to hold in rational homotopy and in the mod p Massey-Peterson case.
2. Find an algebraic description of the first obstruction living in Andre-Quillen cohomology (AQC) to the existence of a realization of unstable coalgebras.
3. Define natural operations on AQC of unstable coalgebras with general coefficients.
As part of the risk management we describe two further fallback projects:
4. Study the Goodwillie tower of the identity functor of simplicial unstable algebras and relate its layers to AQC.
5. Describe the algebra of homotopy operations on simplicial commutative algebras for odd primes p.
These projects are parts of a program of the ER to investigate realization problems and rigidity results associated to singular (co-)homology. A longterm goal (beyond the time frame of the fellowship) is to develop a deformation theory of unstable (co-)algebras over the Steenrod algebra and their realizing homotopy types in the mod p case.
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. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences computer and information sciences software
- natural sciences mathematics pure mathematics algebra commutative algebra
- natural sciences computer and information sciences computational science
- natural sciences mathematics pure mathematics topology algebraic topology
- social sciences sociology governance crisis management
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
MSCA-IF-EF-ST - Standard EF
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) H2020-MSCA-IF-2014
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
93430 VILLETANEUSE
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.