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Homotopy Coherent Category Theory
, 1996
"... this paper we try to lay some of the foundations of such a theory of categories `up to homotopy' or more exactly `up to coherent homotopies'. The method we use is based on earlier work on: ..."
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Cited by 27 (7 self)
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this paper we try to lay some of the foundations of such a theory of categories `up to homotopy' or more exactly `up to coherent homotopies'. The method we use is based on earlier work on:
LATTICE GAUGE FIELD THEORY
, 2001
"... The inspiration for this thesis comes from mathematical physics, especially path integrals and the ChernSimons action. Path integrals were introduced by Feynman in late 1940’s and they have recently been applied to purely geometric problems. The work [33] of Edward Witten on the topological quantum ..."
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Cited by 1 (1 self)
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The inspiration for this thesis comes from mathematical physics, especially path integrals and the ChernSimons action. Path integrals were introduced by Feynman in late 1940’s and they have recently been applied to purely geometric problems. The work [33] of Edward Witten on the topological quantum field theory has been found very attractive by many enthusiastic
STRONG EXPANSIONS FOR TRIADS OF SPACES
"... Abstract. Lisica and Mardesic introduced the notion of coherent expansion of a space to develop a strong shape theory for arbitrary topological spaces. Mardesic then introduced the notion of strong ANRexpansion of a space, which is an intermediate notion between ANRresolution and ANRexpansion, ..."
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Abstract. Lisica and Mardesic introduced the notion of coherent expansion of a space to develop a strong shape theory for arbitrary topological spaces. Mardesic then introduced the notion of strong ANRexpansion of a space, which is an intermediate notion between ANRresolution and ANRexpansion, and showed that this notion can be used to dene the same strong shape category. The purpose of this paper is to generalize those notions to triads of spaces and show that resolutions of triads are strong expansions of triads and that strong expansions of triads are coherent expansions of triads. Hence the strong shape theory for triads is wellde ned, and all notions and results on strong expansions generalize to triads of spaces. As an invariant, strong homotopy groups for triads are de ned, and the excision property with respect to strong homotopy groups and MayerVietoris sequences for strong homology groups are discussed. 1.