Counterexamples to the Kneser conjecture in dimension four |
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Authors: | Matthias Kreck Wolfgang Lück Peter Teichner |
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Institution: | 1. Fachbereich Mathematik, Johannes Gutenberg-Universit?t, 55099, Mainz, Bundesrepublik Deutschland 2. Mathematisches Forschungsinstitut Oberwolfach, 77709, Oberwolfach-Walke, Bundesrepublik Deutschland 3. University of California, San Diego 4. Department of Mathematics, 9500 Gilman Drive, 92093-0112, LaJolla, CA, U.S.A.
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Abstract: | We construct a connected closed orientable smooth four-manifold whose fundamental group is the free product of two non-trivial
groups such that it is not homotopy equivalent toM
0#M
1 unlessM
0 orM
1 is homeomorphic toS
4. LetN be the nucleus of the minimal elliptic Enrique surfaceV
1(2, 2) and putM=N∪
∂NN. The fundamental group ofM splits as ℤ/2 * ℤ/2. We prove thatM#k(S
2×S2) is diffeomorphic toM
0#M
1 for non-simply connected closed smooth four-manifoldsM
0 andM
1 if and only ifk≥8. On the other hand we show thatM is homeomorphic toM
0#M
1 for closed topological four-manifoldsM
0 andM
1 withπ
1(Mi)=ℤ/2. |
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Keywords: | |
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