Skip to main content
European Commission logo
English English
CORDIS - EU research results
CORDIS
CORDIS Web 30th anniversary CORDIS Web 30th anniversary

From Hodge theory to combinatorics and geometry

Objective

We propose an approach to the Dodziuk-Singer conjecture, a central conjecture in geometric topology, specifically concerning the great challenge that understanding aspherical manifolds can pose, based on newly developed tools from combinatorial commutative algebra and combinatorial Hodge Theory, and discuss several intermediate problems along the way. The main idea is based on a connection to
commutative algebra via the partition complex, an interpretation of local cohomology that allows for a translation between data contained in the L2 cohomology of a manifold and Lefschetz properties of toric varieties associated to them.
Additionally, we outline connections to other approaches to the Dodziuk-Singer conjecture as well as special cases, such as the Hopf and Charney-Davis conjectures, and propose ideas to connect the different aspects of the viewpoints into one.
Finally, we discuss problems related to the methods proposed, in particular focussing on unrealised and unexploited relations between combinatorics, Hodge theory and geometry. We discuss in particular deformations of polyhedra and metrics, as well as expansion and connectivity.

Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Net EU contribution
€ 1 334 723,19
Address
RUE MICHEL ANGE 3
75794 Paris
France

See on map

Region
Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
Links
Total cost
€ 1 334 723,19

Beneficiaries (2)