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In work related to positive scalar curvature, Stephan Stolz (Ann. Math.), but later Stolz-Kreck ($HP2$ bundles and Elliptic cohomology) introduced a version of Real connective $K$-homology by consi …

The first non vanishing differential $d_3$ of the cohomological Atiyah-Hirzebruch spectral sequence for computing (Complex) Topological $K$-theory out of ordinary cohomology has a des …

Is there a treatment in the literature of the structure sets relating simple homotopy equivalences to homeomorphisms in the three dimensional case? I am aware that due to the geo …

Due to work of Stanley Kochman in "Integral cohomology operations. Current trends in algebraic topology, Part 1 (London, Ont., 1981), pp. 437–478, CMS Conf. Proc., 2, Amer. Math. Soc., Providence, …

Is there a known relation between the space of units of a ring spectrum, from stable homotopy theory in the sense of Ando-Blumberg-Gepner https://arxiv.org/pdf/1002.3004v2.pdf and …

Can someone explain the relationship between reduced and unreduced parametrized homology theories in the parametrized setting à la May-Sigurdsson with maps to a reference space $B$?. Is it just a co …

Consider a locally trivial (topological) bundle over the Klein bottle $$ I\to E \to K$$ The projection map $E \to K$ is a homotopy equivalence. Is it a simple homotopy equivalence? Du …

Steenrod's problem asks wheter a simplicial homology class of a topological space $x$, $$ x\in H_n(X, \mathbb{Z})$$ can be represented by a triangulation of an $n$-dimensional, close …

In a Commentarii Mathematici Helvetici paper by Benno Eckman and Heinz Müller in 1980 (volume 50, pages 510-520) proved that poincaré Duality Groups of dimension 2 with positive first Bet …

It is known in elementary algebraic topology that a covering map induces an isomorphism of higher homotopy groups. Is there any relation of the higher homotopy groups of the …

Are the Atiyah-Bott-Shapiro Orientation and the Anderson-Brown-Peterson Splitting compatible in any sense? The first guess is that the ABS-Orientation is related to the projections o …

In a remarkable series of papers, both anticipating development in geometric topology and algebraic K-theory, specifically what we call now the Farrell-Jones conjecture, Waldhausen intr …

Where can I find a comprehensive survey of computations of equivariant stems? To my knowledge, the status is: Classical Work of Araki and Iriye, Osaka J. Math. 19 (1982). Comput …

The mod 2 cohomology of the connective ko spectrum is known to be the module $\mathcal{A}\otimes_{\mathcal{A}_2} \mathbb{F}_{2}$, where $\mathcal{A}$ denotes the Steenrod algebra, and …

It is historically known that Jean Leray gave a course on algebraic topology while captive in the Officer's detention camp XVI in Edelbach, Austria during WW2. (References to this topic …