Publications and Preprints

 

Papers:

1. A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007), 2043-2058.
    (math.AT/0406507)

2. Three models for the homotopy theory of homotopy theories, Topology 46 (2007), 397-436.
    (math.AT/0504334)
    Longer thesis version (University of Notre Dame, 2005)

3. Rigidification of algebras over multi-sorted theories, Algebr. Geom. Topol. 6 (2006) 1925-1955.
    (math.AT/0508152)

4. Simplicial monoids and Segal categories, Contemp. Math. 431 (2007)  59-83.
    and correction
    (math.AT/0508416; math.AT/0806.1767)

5. A characterization of fibrant Segal categories, Proc. Amer. Math. Soc. 135 (2007) 4031-4037.
    (math.AT/0603400)

6. A survey of (∞,1)-categories, in J. Baez and J. P. May, Towards Higher Categories, IMA Volumes in Mathematics and Its Applications, Springer, 2010, 69-83.
    (math.AT/0610239)

7. Adding inverses to diagrams encoding algebraic structures, Homology, Homotopy Appl. 10(2), 2008, 149–174.
    (math.AT/0610291)

8. Complete Segal spaces arising from simplicial categories, Trans. Amer. Math. Soc. 361 (2009), 525-546.
    (math.AT/0704.1624)

9. Adding inverses to diagrams II: Invertible homotopy theories are spaces, Homology, Homotopy Appl. 10(2), 2008, 175–193.
    (math.AT/0710.2254)

10. Homotopy fiber products of homotopy theories, Israel Journal of Mathematics 185 (2011), 389-411.

     (math.AT/0811.3175)

 

11. Derived Hall algebras for stable homotopy theories, Cah. Topol. Géom. Différ. Catég. 54 (2013), no. 1, 28–55.     

      (math.AT/0910.1861)

 

12. Homotopy limits of model categories and more general homotopy theories, Bull. Lond. Math. Soc. 44 (2012), no. 2, 311–322.

      (math.AT/1010.0717)

 

13. Models for (∞, n)-categories and the cobordism hypothesis, in H. Sati and U. Schreiber, ed., Mathematical Foundations of Quantum Field Theory and Perturbative String Theory, Proc. Sympos. Pure Math. 83 (2011) 17-30.

     (math.AT/1011.0110)

 

14. Groupoid cardinality and Egyptian fractions (with C. Walker), to appear in College Mathematics Journal.

      (older, more formal version)   

 

15. Reedy categories and the θ-construction (with C. Rezk), Math. Z. 274 (1), 2013, 499-514.

      (math.AT/1110.1066)

 

16. Comparison of models for (∞,n)-categories, I (with C. Rezk), Geom. Topol. 17 (2013), no. 4, 2163–2202.

      (math.AT/1204.2013)

 

17. Reedy categories which encode the notion of category actions (with P. Hackney)

      (math.AT/1207.3467)

 

18. Group actions on Segal operads (with P. Hackney), to appear in Israel Journal of Mathematics.

      (math.AT/1207.3465)

 

19. Homotopy colimits of model categories, to appear in Arolla proceedings.

      (math.AT/1212.4541)

 

20. Group actions on Γ-spaces (with P. Hackney)

      (math.AT/1212.4542)

 

21. Cluster categories for topologists (with M. Robertson)

      (math.AT/1308.2560)

 

22. Fixed points of p-toral groups acting on partition complexes (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren)

      (math.AT/1401.0491)

 


 

Unpublished Notes:

 

Workshop on the homotopy theory of homotopy theories



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http://www.math.ucr.edu/~jbergner/papers.html                                                       Last modified: 3 January 2014