Rigidity implication of the Novikov conjecture

Part of my own research is related to the Novikov conjecture, and hence I am always interested to see applications of it. When reading the preprint Essentiality and simplicial volume of manifolds fibered over spheres by Thorben Kastenholz and Jens Reinhold (arXiv:2107.05892) I saw another one of these applications (Theorem D therein). I do not … Continue reading "Rigidity implication of the Novikov conjecture"

Space of psc-metrics on non-spin manifolds

Recently I was having a look at the preprint Essentiality and simplicial volume of manifolds fibered over spheres by Thorben Kastenholz and Jens Reinhold (arXiv:2107.05892). In Theorem C therein they construct a closed, totally non-spin manifold (i.e., one whose universal cover is even not spin) whose space of Riemannian metrics of positive scalar curvature has … Continue reading "Space of psc-metrics on non-spin manifolds"

A question about the first \(L^2\)-Betti number

In a recent arXiv preprint (arxiv:2106.15750) J. A. Hillman discusses a new homological approach towards some old results on 3-manifold groups due to Elkalla. In his article he runs into an interesting question concerning the first \(L^2\)-Betti number of finitely generated groups: Assume that a finitely generated group G has infinite subgroups \(N\leq U\) such … Continue reading "A question about the first \(L^2\)-Betti number"

Computer assisted verification of contemporary mathematics

Half a year ago Steffen Kionke wrote a blog post on condensed mathematics wherein he mentioned that Peter Scholze put up a challenge to formally verify a key fundamental result of a joint paper with Clausen: a result Scholze terms his most important theorem to date. Today I want to inform you that the mentioned … Continue reading "Computer assisted verification of contemporary mathematics"

A hyperbolic 5-manifold which fibres over the circle and subgroups of hyperbolic groups

Recently appeared a highly interesting paper by Italiano, Martelli, Migliorini on the arXiv (2105.14795) (Okay, this was already three weeks ago – I don’t follow the “geometric topology” – and someone had to point me there). The paper solves at least two longstanding open problems by studying an explicit 5-dimensional hyperbolic manifold. It is well-known … Continue reading "A hyperbolic 5-manifold which fibres over the circle and subgroups of hyperbolic groups"

GDM-Monat 2021 – Vortrag zur Doppelten Diskontinuität

Auf dem GDM-Monat im März 2021 (voriger Beitrag dazu: link) hörte ich auch den Vortrag von Viktor Isaev zu dem Thema: Entwicklungsverläufe von Studierenden bezüglich ihrer Wahrnehmung zur doppelten Diskontinuität. Was diese Doppelte Diskontinuität ist, erklärt man am besten mit folgendem Zitat von Felix Klein: Der junge Student sieht sich am Beginn seines Studiums vor … Continue reading "GDM-Monat 2021 – Vortrag zur Doppelten Diskontinuität"

GDM-Monat 2021 – Hauptvortrag zum Mathematischen Beweisen

Die Gesellschaft für Didaktik der Mathematik (GDM) hat wegen der Corona-Pandemie anstatt einer Präsenztagung im Jahre 2021 im März einen Monat lang Vorträge und Veranstaltungen ‘dezentral und online’ durchgeführt (link). In manche der Vorträge hatte ich damals reingehört (hauptsächlich solche, die sich mit der Hochschuldidaktik beschäftigen) und wollte auf diesem Blog kurz über die Inhalte … Continue reading "GDM-Monat 2021 – Hauptvortrag zum Mathematischen Beweisen"