Rational homotopy of non-connected spacesmat.uab.cat/~SYTM/pdf/sytm-Buijs.pdf · Urtzi Buijs (Joint...
Transcript of Rational homotopy of non-connected spacesmat.uab.cat/~SYTM/pdf/sytm-Buijs.pdf · Urtzi Buijs (Joint...
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II Spanish Young Topologists Meeting.Barcelona, December 2013.
Rational homotopy of non-connected
spaces
Urtzi Buijs(Joint work with Aniceto Murillo)
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Nord Pas de Calais/Belgium Congress of MathematicsValenciennes, October 2013
Rational homotopy of non-connected
spaces
Urtzi Buijs(Joint work with Aniceto Murillo)
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1. A brief introduction
Theorem Sullivan, Publications Mathématiques de l’IHÉS 1977 Bousfield, Guggenheim, Mem. Amer. Math. Soc. 1976
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Theorem
1. A brief introduction
Quillen, Annals of Mathematics, 1969
Neisendorfer, Pacific J. of Math. 1978
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Theorem
1. A brief introduction
Theorem
Haefliger, Trans. of the Amer. Math. Soc. 1982Brown, Szczarba, Trans. of the Amer. Math. Soc. 1997
Scherer, Tanré, Arch. Math. 1992B. , Félix, Murillo, Trans. of the Amer. Math. Soc. 2009
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Goal
1. A brief introduction
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2. Cochain functor
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2. Cochain functor
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2. Cochain functor
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2. Cochain functor
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2. Cochain functor
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2. Cochain functor
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2. Cochain functor
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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3. Points, augmentations and Maurer-Cartan elements.
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4. Lawrence-Sullivan interval and homotopy
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4. Lawrence-Sullivan interval and homotopy
R. Lawrence, D. Sullivan
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4. Lawrence-Sullivan interval and homotopy
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4. Lawrence-Sullivan interval and homotopy
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4. Lawrence-Sullivan interval and homotopy
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4. Lawrence-Sullivan interval and homotopy
B., Murillo, Adv. In Math 2013
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5. Algebraic models of non-connected spaces
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Lemma
5. Algebraic models of non-connected spaces
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Lemma
Theorem
Theorem
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Merci!