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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 3

On minimal Poincaré 4-complexes

Alberto CAVICCHIOLI
Friedrich HEGENBARTH
Duşan REPOVŞ
Pages
535–557
Publication Date
2014-05-16
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the present paper we study existence and uniqueness questions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We consider 2 types of minimal Poincaré 4-complexes.
📊
Key Findings & Data:One is defined with respect to the degree 1-map order.
💡
Conclusion & Impact:In the present paper we study existence and uniqueness questions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Poincaré 4-complex · equivariant intersection form · degree 1-map

Abstract

We consider 2 types of minimal Poincaré 4-complexes. One is defined with respect to the degree 1-map order. This idea was already present in our previous papers, and more systematically studied later by Hillman. The second type of minimal Poincaré 4-complexes was introduced by Hambleton, Kreck, and Teichner. It is not based on an order relation. In the present paper we study existence and uniqueness questions.

Özet

We consider 2 types of minimal Poincaré 4-complexes. One is defined with respect to the degree 1-map order. This idea was already present in our previous papers, and more systematically studied later by Hillman. The second type of minimal Poincaré 4-complexes was introduced by Hambleton, Kreck, and Teichner. It is not based on an order relation. In the present paper we study existence and uniqueness questions.

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Cite This Article

CAVICCHIOLI, A., HEGENBARTH, F., REPOVŞ, D. (2014). On minimal Poincaré 4-complexes. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 3, 535–557. https://ajindex.com/articles/185734

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References (15)

  1. Baues, H.J.: Combinatorial Homotopy and 4 -Dimensional Complexes. Berlin. Walter de Gruyter 1991.
  2. Cavicchioli, A., Hegenbarth, F.: On 4 -manifolds with free fundamental groups. Forum Math. 6, 415–429 (1994).
  3. Cavicchioli, A., Hegenbarth, F., Repov˘ s, D.: Four–manifolds with surface fundamental groups. Trans. Amer. Math. Soc. 349, 4007–4019 (1997).
  4. Hambleton, I., Kreck, M.: On the classification of topological 4 -manifolds with finite fundamental group. Math. Ann. 280, 85–104 (1988).
  5. Hambleton, I., Kreck, M., Teichner, P.: Topological 4 -manifolds with geometrically 2 -dimensional fundamental group. J. Topology Anal. 1, 123–151 (2009).
  6. Hegenbarth, F., Piccarreta, S.: On Poincar´ e 4 -complexes with free fundamental groups. Hiroshima Math. J. 32, 145–154 (2002).
  7. Hegenbarth, F., Repov˘ s, D., Spaggiari, F.: Connected sums of 4 -manifolds. Topology Appl. 146–147, 209–225 (2005).
  8. Hillman, J.A.: P D 4 -complexes with strongly minimal models. Topology Appl. 153, 2413–2424 (2006).
  9. Hillman, J.A.: Strongly minimal P D 4 -complexes. Topology Appl. 156, 1565–1577 (2009).
  10. Kaplansky, I.R.: Fields and Rings. Chicago. University of Chicago Press 1969
  11. MacLane, S., Whitehead, J.H.C.: On the 3–type of a complex. Proc. Nat. Acad. Sci. 36, 41–48 (1950)
  12. Pamuk, M.: Homotopy self-equivalences of 4 -manifolds with PD 2 -fundamental group. Topology Appl. 156, 1445– 1458 (2009).
  13. Wall, C.T.C.: Poincar´ e complexes. Ann. of Math. 86, 213–245 (1967).
  14. Wall, C.T.C.: Surgery on Compact Manifolds. London. Academic Press 1970
  15. Whitehead, J.H.C.: On a certain exact sequence. Ann. of Math. 52 (2), 51–110 (1950).