Publications and Preprints

 

Research 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.      Adding inverses to diagrams encoding algebraic structures, Homology, Homotopy Appl. 10(2), 2008, 149–174.

(math.AT/0610291)

and erratum

 

7.      Complete Segal spaces arising from simplicial categories, Trans. Amer. Math. Soc. 361 (2009), 525-546.

(math.AT/0704.1624)

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

(math.AT/0710.2254)

and erratum   

 

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

(math.AT/0811.3175)

 

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

(math.AT/0910.1861)

 

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

(math.AT/1010.0717)

 

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

(math.AT/1110.1066)

 

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

(math.AT/1204.2013)

 

14.  Reedy categories which encode the notion of category actions (with P. Hackney), Fund. Math.  228 (2015), no. 3, 193–222.

(math.AT/1207.3467)

 

15.  Group actions on Segal operads (with P. Hackney), Israel J. Math. 202 (2014), no. 1, 423–460. 

(math.AT/1207.3465)

 

16.  Homotopy colimits of model categories, An Alpine Expedition through Algebraic Topology, Contemp. Math., 617 (2014), 31-37.

(math.AT/1212.4541)

 

17.  Group actions on Γ-spaces (with P. Hackney), Manifolds and K-Theory, Contemp. Math, 682 (2017) 39-50.

(math.AT/1212.4542)

 

18.  Fixed points of p-toral groups acting on partition complexes (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren), Women in Topology: Collaborations in Homotopy Theory, Contemp. Math. 641 (2015), 83-96. 

(math.AT/1401.0491)

 

19.  Classification of problematic subgroups of U(n) (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren), to appear in Trans. Amer. Math. Soc.  

(math.AT/1407.0062)

 

20.  Equivalence of models for equivariant (∞,1)-categories, Glasg. Math. J., 59 (2017), no. 1, 237–253. 

(math.AT/1408.0038)

 

21.  Equivariant complete Segal spaces (with S.G. Chadwick), Homology, Homotopy, and Appl. 17(2), 2015, 371-381. 

(math.AT/1502.06637)

 

22.   2-Segal sets and the Waldhausen construction (with A. Osorno, V. Ozornova, M. Rovelli, and C.I. Scheimbauer), Topology Appl.,235 (2018) 445--484.

(math.AT/1609.02853)


Book:

The Homotopy Theory of (∞,1)-Categories, Cambridge University Press, 2018.

(By my contract, I can make the pdf available freely 1 year after publication, so a version will be made available here in March 2019.)


Expository Papers:

1.      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)

 

2.      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)

 

3.      Cluster categories for topologists (with M. Robertson), Stacks and Categories in Geometry, Topology and Algebra, Contemp. Math. 643 (2015) 25-35.

(math.AT/1308.2560)


Papers written for or with undergraduates:

1.      Groupoid cardinality and Egyptian fractions (with C. Walker), College Math. J. 46 (2015) 122-129.

(older, more formal version)

 

2.      Action graphs and Catalan numbers (with G. Alvarez and R. Lopez), J. Integer Seq. 18 (2015), Article 15.7.2.

(math.CO/1503.00044)


Submitted preprints:

1.      Comparison of models for (∞,n)-categories, II (with C. Rezk)

(math.AT/1406.4182)

 

2.      Action graphs, planar rooted forests, and self-convolutions of the Catalan numbers (with C. Harper, R. Keller, and M. Rosi-Marshall)

(math.CO/1807.03005)

 


Unpublished Notes:

Workshop on the homotopy theory of homotopy theories



Return to Julie Bergner's web page

 


 

http://www.people.virginia.edu/~jeb2md/papers.html                  Last modified: 13 July 2018