# Topological manifolds and real algebraic geometry

Bollettino dell'Unione Matematica Italiana (2003)

- Volume: 6-B, Issue: 3, page 545-555
- ISSN: 0392-4033

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topTognoli, Alberto. "Topological manifolds and real algebraic geometry." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 545-555. <http://eudml.org/doc/194830>.

@article{Tognoli2003,

abstract = {We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological $4$-manifolds.},

author = {Tognoli, Alberto},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {10},

number = {3},

pages = {545-555},

publisher = {Unione Matematica Italiana},

title = {Topological manifolds and real algebraic geometry},

url = {http://eudml.org/doc/194830},

volume = {6-B},

year = {2003},

}

TY - JOUR

AU - Tognoli, Alberto

TI - Topological manifolds and real algebraic geometry

JO - Bollettino dell'Unione Matematica Italiana

DA - 2003/10//

PB - Unione Matematica Italiana

VL - 6-B

IS - 3

SP - 545

EP - 555

AB - We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological $4$-manifolds.

LA - eng

UR - http://eudml.org/doc/194830

ER -

## References

top- AKBULUT, S.- KING, H., The topology of real algebraic sets with isolated singularities, Ann. of Math., 113 (1981), 425-446. Zbl0494.57004MR621011
- BENEDETTI, R.- RISLER, J. J., Real algebraic and semialgebraic sets, Hermann, Paris (1990). Zbl0694.14006MR1070358
- BERETTA, L., Extension of maps and ordering, Ann. Univ. Ferrara, 44 (1998), 9-25. Zbl0952.54010MR1744138
- CAVICCHIOLI, A., Sulla classificazione topologica delle varietà, Boll. Un. Mat. Ital. (7), 9-B (1995), 633-682. Zbl0857.57019
- CAVICCHIOLI, A.- HEGENBARTH, F.- SPAGGIARI, F., A splitting theorem for homotopy equivalent smooth $4$-manifolds, Rendiconti di Matematica Ser. VII, 17 (1997), 523-539. Zbl0890.57032MR1608716
- CURTIS, C. L.- FREEDMAN, M. H.- HSIANG, W. C.- STONG, R., A decomposition theorem for $h$-cobordant smooth simply-connected compact $4$-manifolds, Invent. Math., 123 (1996), 343-348. Zbl0843.57020MR1374205
- DONALDSON, S., An application of gauge theory to four-dimensional topology, J. Differential Geom., 18 (1983), 269-315. Zbl0507.57010MR710056
- DONALDSON, S., Connections, cohomology and the intersection forms of $4$-manifolds, J. Differential Geom., 24 (1986), 275-341. Zbl0635.57007MR868974
- DONALDSON, S., The orientation of Yang-Mills moduli spaces and four-dimensional topology, J. Differential Geom., 26 (1987), 397-428. Zbl0683.57005MR910015
- DONALDSON, S., Irrationality and the $h$-cobordism conjecture, J. Differential Geom., 26 (1987), 141-168. Zbl0631.57010MR892034
- FREEDMAN, M. H., The topology of four-dimensional manifolds, J. Differential Geom., 17 (1982), 357-453. Zbl0528.57011MR679066

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