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Hiroki Kodama, Peter W. Michor (2006)
Revista Matemática Complutense
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The space B = Imm (S, R) / Diff (S) of all immersions of rotation degree 0 in the plane modulo reparameterizations has homotopy groups π(B ) = Z, π(B ) = Z, and π(B ) = 0 for k ≥ 3.
Teichmann, Josef (2004)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Michael Weiss (2008)
Archivum Mathematicum
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The Mumford conjecture predicts the ring of rational characteristic classes for surface bundles with oriented connected fibers of large genus. The first proof in [11] relied on a number of well known but difficult theorems in differential topology. Most of these difficult ingredients have been eliminated in the years since then. This can be seen particularly in [7] which has a second proof of the Mumford conjecture, and in the work of Galatius [5] which is concerned mainly with a “graph”...
Oleg Myasnichenko (1996)
Banach Center Publications
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Diarmuid J. Crowley, Peter D. Zvengrowski (2008)
Archivum Mathematicum
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In this note we give examples in every dimension of piecewise linearly homeomorphic, closed, connected, smooth -manifolds which admit two smoothness structures with differing spans, stable spans, and immersion co-dimensions. In dimension the examples include the total spaces of certain -sphere bundles over . The construction of such manifolds is based on the topological variance of the second Pontrjagin class: a fact which goes back to Milnor and which was used by Roitberg to...