2021년 2월 17일 (수) 07:47에 Pythagoras0님의 편집

2021-02-17T07:47:52Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T12:05:38Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2020-12-22T06:21:41Z

노트: 새 문단

새 문서

== 노트 ==

===위키데이터===
* ID : [https://www.wikidata.org/wiki/Q31839400 Q31839400]
===말뭉치===
# This provides a direct proof of the relation between the Alexander polynomial and analytic and Reidemeister torsions.<ref name="ref_7b09e5c2">[https://www.sciencedirect.com/science/article/pii/0393044094900221 Reidemeister torsion, the Alexander polynomial and U (1,1) Chern-Simons theory]</ref>
# Analytic torsion (or Ray–Singer torsion) is an invariant of Riemannian manifolds defined by Daniel B. Ray and Isadore M. Singer (1971, 1973a, 1973b) as an analytic analogue of Reidemeister torsion.<ref name="ref_c54480f7">[https://en.wikipedia.org/wiki/Analytic_torsion Analytic torsion]</ref>
# Reidemeister torsion is closely related to Whitehead torsion; see (Milnor 1966).<ref name="ref_c54480f7" />
# Reidemeister torsion was first used to combinatorially classify 3-dimensional lens spaces in (Reidemeister 1935) by Reidemeister, and in higher-dimensional spaces by Franz.<ref name="ref_c54480f7" />
# It proves that for such representations the notion of Reidemeister torsion is well-defined.<ref name="ref_73261b2d">[https://aip.scitation.org/doi/10.1063/1.5021318 A note on exceptional groups and Reidemeister torsion]</ref>
# The author defines the higher Franz-Reidemeister torsion based on Volodin's K-theory and Borel's regulator map.<ref name="ref_21f2227c">[https://cds.cern.ch/record/2279763 Higher Franz-Reidemeister torsion]</ref>
# In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of contexts.<ref name="ref_952aaaf0">[https://mathworld.wolfram.com/ReidemeisterTorsion.html Reidemeister Torsion -- from Wolfram MathWorld]</ref>
# At the time of its discovery, the Reidemeister torsion was the first 3-manifold invariant able to distinguish between manifolds which are homotopy equivalent but not homeomorphic.<ref name="ref_952aaaf0" />
# Another common context for which to define Reidemeister torsion is in the case of CW-complexes.<ref name="ref_952aaaf0" />
# In this context, the Reidemeister torsion is a well-defined element of .<ref name="ref_952aaaf0" />
# N2 - The goal of this article is to prove the product formula for parametrized homotopy Reidemeister torsion.<ref name="ref_05e67a55">[https://pennstate.pure.elsevier.com/en/publications/the-product-theorem-for-parametrized-homotopy-reidemeister-torsio The product theorem for parametrized homotopy Reidemeister torsion]</ref>
# AB - The goal of this article is to prove the product formula for parametrized homotopy Reidemeister torsion.<ref name="ref_05e67a55" />
# The Reidemeister torsion approach also provides a natural approach to proving and extending certain monotonicity results of Cochran and Harvey.<ref name="ref_68731f42">[https://msp.org/pjm/2007/230-2/p02.xhtml Pacific Journal of Mathematics Vol. 230, No. 2, 2007]</ref>
# We conjecture a version of the Cheeger-Müller theorem, namely that the combinatorial Reidemeister torsion coincides with the analytic torsion defined by Mathai and Wu.<ref name="ref_bf9e4f45">[https://orbilu.uni.lu/handle/10993/22562 Reidemeister torsion for flat superconnections]</ref>
===소스===
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 * ID :  [https://www.wikidata.org/wiki/Q31839400 Q31839400]

← 이전 판		2020년 12월 26일 (토) 12:05 판
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		+	* ID : [https://www.wikidata.org/wiki/Q31839400 Q31839400]

Reidemeister torsion - 편집 역사

2021년 2월 17일 (수) 07:47에 Pythagoras0님의 편집

Pythagoras0: /* 메타데이터 */ 새 문단

Pythagoras0: /* 노트 */ 새 문단