Localizable invariants of combinatorial manifolds and Euler characteristic
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- 作者：Li Yu (1)
- 关键词：57R05 ; 57R20 ; 57Q99 ; Combinatorial manifold ; Localizable invariant ; Euler characteristic ; Local formula
- 刊名：Archiv der Mathematik
- 出版年：2014
- 出版时间：February 2014
- 年：2014
- 卷：102
- 期：2
- 页码：191-200
- 全文大小：259 KB
- 参考文献：1. A. Brondsted, An introduction to convex polytopes, Graduate Texts in Mathematics, vol. 90, Springer-Verlag, New York, 1983
2. V. M. Buchstaber and T. E. Panov, Torus actions and their applications in topology and combinatorics, University Lecture Series, 24. American Mathematical Society, Providence, RI, 2002.
3. Gaifullin A. A.: Computation of characteristic classes of a manifold from a triangulization of it. Uspekhi Matem. nauk 60, 37鈥?6 (2005) CrossRef
4. Gaifullin A. A.: Computation of characteristic classes of a manifold from a triangulization of it, English transl. Russian Math. Surveys 60, 615鈥?44 (2005) CrossRef
5. Klee V.: A combinatorial analogue of Poincar茅鈥檚 duality theorem. Canad. J. Math. 16, 517鈥?31 (1964) CrossRef
6. U. Pachner, Konstruktionsmethoden und das kombinatorische Hom枚omorphieproblem f眉r Triangulationen kompakter semilinearer Mannigfaltigkeiten, Abh. Math. Sem. Univ. Hamburg 57 (1986), 69鈥?5.
7. Roberts J.: Unusual formulae for the Euler characteristic. J. Knot Theory Ramifications 11, 793鈥?96 (2002) CrossRef
8. C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, 2nd ed., Springer-Verlag, Berlin 1982.
9. Yu L.: A property that characterizes Euler characteristic among invariants of combinatorial manifolds. Adv. Math. 225, 794鈥?04 (2010) CrossRef - 作者单位：Li Yu (1)
1. Department of Mathematics and IMS, Nanjing University, Nanjing, 210093, People鈥檚 Republic of China - ISSN：1420-8938
文摘
It is shown that if a real-valued PL-invariant of closed combinatorial manifolds admits a local formula that depends only on the f-vector of the link of each vertex, then the invariant must be a constant times the Euler characteristic.