Geometry at Infinity

Priority programme of the DFG

Welcome to SPP 2026

This is the platform of a coordinated research programme in mathematics, funded by the German Research Foundation (DFG).  It comprises 80 research projects in the fields of differential geometry, geometric topology, and global analysis. More than 80 researchers from doctoral to professorial level and based at more than 20 German and Swiss universities are represented in this programme. 

Latest Blog posts

PSC obstructions via infinite width and index theory In a recent preprint (arXiv:2108.08506), Yosuke Kubota proved an intriguing new result on the relation of largeness properties of spin manifolds and index-theoretic obstructions to positive scalar curvature (psc): Let \(M\) be a closed spin \(n\)-manifold. If \(M\) has infinite \(\mathcal{KO}\)-width, then its Rosenberg index \(\alpha(M) \in \mathrm{KO}_n(\mathrm{C}^\ast_{\max} \pi_1 M)\) does not vanish. Let us … Continue reading "PSC obstructions via infinite width and index theory"
(Non-)Vanishing results for Lp-cohomology of semisimple Lie groups For a locally compact, second countable group \(G\) one can define the continuous \(L^p\)-cohomology \(H^*_{ct}(G,L^p(G))\) of \(G\) and the reduced version \(\overline{H}^*_{ct}(G,L^p(G))\) for all \(p > 1\). In his influential paper “Asymptotic invariants of infinite groups” Gromov asked if \[H^j(G,L^p(G)) = 0 \] when \(G\) is a connected semisimple Lie group and \(j < \mathrm{rk}_{\mathbb{R}}(G)\). … Continue reading "(Non-)Vanishing results for Lp-cohomology of semisimple Lie groups"
New book about Freedman’s proof Today I learnt from an article in the QuantaMagazine (link to article) that there is finally a new book trying to explain Freedman’s proof of the 4-dimensional Poincaré conjecture (link to book). The article is fun to read since it contains statements of the involved people about how the whole ‘situation’ about the non-understandable write-up … Continue reading "New book about Freedman’s proof"

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