This was a seminar course on the theory of topological manifolds, in which the participants gave the talks.

Notes from the talks will contribute to the lecture notes project from the
previous lecture course.

Lecture notes after the seminar, including notes from the talks below.

List of topics and schedule.

Notes from talks:

Topological manifolds are Euclidean Neighbourhood Retracts by Raphael Floris.

The Alexander horned sphere and Bing's hooked rug by Franca Lippert.

The double suspension of the Mazur homology 3-sphere by Fadi Mezher.

Finding a boundary for an open manifold by Alice Merz.

Homotopy invariance for microbundles by Cara Hobohm.

Counting topological manifolds by Magdalina Von Wunsch.

The engulfing theorem and uniqueness of PL structures on Euclidean space of dimension at least 5 by Diego Santoro.

A non PL-able manifold by Ekin Ergen.

Rochlin's theorem by Christian Kremer.

Explicit immersions of a punctured n-torus in ℝ^{n} and Kirby's torus trick for surfaces and 3-manifolds by Daniel Galvin, Weizhe Niu, and Benjamin Ruppik.

Talks were streamed through Zoom. Some recordings were made available afterwards, depending on the wishes of the speaker.
Bonn participants: check eCampus, others please email us for access to the recordings.

Time: 1015-1200, German time.

Dates: Wednesdays, April 21st 2021 - July 23rd 2021.

Contact details:

mark.a.powell@durham.ac.uk

aruray@mpim-bonn.mpg.de

General resources

Rob Kirby's lectures, Edinburgh, November 2012.

Andrew Ranicki's collection of references.

Foundational essays on topological manifolds, smoothings, and triangulations by R. Kirby and L. Siebenmann.

Geometric topology notes by S. Ferry.

Recent advances in topological manifolds by A. Casson.

Original handwritten version of Casson's lecture notes by A. Ranicki.

Fragments of Geometric Topology from the Sixties by S. Buonchristiano.

Lecture notes on topological manifolds by A. Kupers.

Counting topological manifolds by J. Cheeger and J. Kister.

Wild embeddings and approximation for embeddings

Some wild cells and spheres in three-dimensional space by E. Artin and R. Fox.

Embeddings in manifolds by R. Daverman and G. Venema.

Topological embeddings by T. B. Rushing.

Collars on boundaries

Locally Flat Imbeddings of Topological Manifolds by M. Brown.

A new proof of Brown's collaring theorem by R. Connelly.

Collars and concordances of topological manifolds by M. Armstrong.

Schoenflies theorem

A proof of the generalized Schoenflies theorem by M. Brown.

The canonical Schoenflies theorem by D.B. Gauld.

Microbundles

Microbundles by J. Milnor.

Microbundles and differentiable structures by J. Milnor.

Microbundles are fibre bundles by J. Kister.

On normal microbundles by M. Hirsch.

An embedding without a normal microbundle by C.P. Rourke and B.J. Sanderson.

Torus trick

Stable homeomorphisms and the annulus conjecture by R. Kirby.

Deformations of Spaces of Imbeddings by R. Edwards and R. Kirby.

The Kirby Torus Trick for Surfaces by A. Hatcher.

The triangulation of 3-manifolds by A.J.S. Hamilton.

On bundles over a sphere with fibre Euclidean space by C.T.C. Wall.

Structures on MxR by W. Browder.

Handles, semihandles, and destabilization of isotopies by D. Webster.

Immersions

Explicit codimension zero immersions of the punctured torus in Euclidean space: by Ferry, Milnor, and Barden.

La classification des immersions combinatoires by A. Haefliger and V. Poénaru.

Immersions and surgeries on topological manifolds by J.A. Lees.

Lees' immersions theorem and the triangulation of manifolds by R. Lashof.

Algebraic Topology proceedings 1971 by A. Liulevicious (ed). See p.131 The immersion approach to triangulation and smoothing by R. Lashof.

Algebraic Topology proceedings Aarhus 1970. See p. 282, The immersion approach to triangulation and smoothing by R. Lashof.

Groups of Automorphisms of Manifolds by D. Burghelea, R. Lashof, and M. Rothenberg. Appendix by E. Pedersen on the topological category.

Homeomorphism groups

Local contractibility of the group of homeomorphisms of a manifold by A.V. Cernavskii.

Homotopy in homeomorphism spaces, TOP and PL by M.-E. Hamstrom.

Homotopy tori

On homotopy tori and the annulus theorem by C.T.C. Wall.

On homotopy tori II by W.C. Hsiang and C.T.C. Wall.

Fake tori, the annulus conjecture, and the conjectures of Kirby by W.C. Hsiang and J. Shaneson.

Fake tori by W.C. Hsiang and J. Shaneson.

The topological rigidity of the torus, MSc thesis of Alexandre Martin.

Stable structures

Stable structures on manifolds by M. Brown and H. Gluck.

Stable structures on manifolds: I Homeomorphisms of S^{n} by M. Brown and H. Gluck.

Stable structures on manifolds: II Stable manifolds by M. Brown and H. Gluck.

Stable structures on manifolds: III Applications by M. Brown and H. Gluck.

Piecewise Linear manifolds

Seminar on combinatorial topology by C. Zeeman.

Piecewise linear topology by J.F.P. Hudson.

Introduction to piecewise-linear topology by C. Rourke and B. Sanderson.

Lectures on polyhedral topology by J. Stallings.

Variétés linéaires par morceaux et variétés combinatoires by C. Dedecker.

Microbundles and bundles I by N. Kuiper and R. Lashof.

Microbundles and bundles II by N. Kuiper and R. Lashof.

Microbundles and smoothing by R. Lashof and M. Rothenberg.

Block bundles: I by C. Rourke and B. Sanderson.

Geometric topology notes by J. Lurie.

Smoothing and PLing theory

Notes on Smoothing theory by J. Davis.

Manifolds and Poincaré complexes by J. Davis and N. Petrosyan.

Piecewise linear structures on topological manifolds by Y. Rudyak.

Triangulations of manifolds I by R. Lashof and M. Rothenberg.

The Hauptvermutung book by A. Ranicki (ed), A. Casson, D. Sullivan, M. Armstrong, C. Rourke, and G. Cooke.

Manifolds - Amsterdam 1970 by N. Kuiper (ed). See first 5 papers.

Topology of manifolds - Proceedings of Georgia Topology conference 1969 by J. Cantrell and C. Edwards (ed). See Chapter 1.

Structures on Euclidean space and the Poincaré conjecture

The piecewise linear structure of Euclidean space by J. Stallings.

Finding a boundary for an open manifold by W. Browder, J. Levine, and G. Livesay.

Polyhedral homotopy spheres by J. Stallings.

The generalised Poincaré conjecture by E. C. Zeeman.

Generalised Poincare's conjecture in dimensions greater than four by S. Smale.

Differentiable and combinatorial structures on manifolds by S. Smale.

The engulfing theorem for topological manifolds by M. H. A. Newman.